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  • HP 50g graphing calculator

    users manual

    HEdition 1

    HP part number F2229AA-90001


    Hewlett-Packard Com4995 Murphy CanyoSuite 301 San Diego,CA 92123

    Printing HistoryEdition 1


    006 Hewlett-Packard Development Company, L.P.ation, or translation of this manual is prohibited permission of Hewlett-Packard Company, except as pyright laws.

    pany n Rd,

    April 2006

  • PrefaceYou have in your hands a compact symbolic and numerical computer that will facilitate calculation and mathematical analysis of problems in a variety of disciplines, from elementary mathematics to advanced engineering and science subjects. This manual contains examples that illustrate the use of the basic calculator functions and operations. The chapters in this users manual are organized by subject in order of difficulty: from the setting of calculator modes, to real and complex number calculations, operations with lists, vectors, and matrices, graphics, calculus applications, vector analysis, differential equations, probability and statistics.For symbolic operations the calculator includes a powerful Computer Algebraic System (CAS), which lets you select different modes of operation, e.g., complex numbers vs. real numbers, or exact (symbolic) vs. approximate (numerical) mode. The display can be adjusted to provide textbook-type expressions, which can be useful when working with matrices, vectors, fractions, summations, derivatives, and integrals. The high-speed graphics of the calculator are very convenient for producing complex figures in very little time.Thanks to the infrared port, the USB port, and the RS232 port and cable provided with your calculator, you can connect your calculator with other calculators or computers. This allows for fast and efficient exchange of programs and data with other calculators and computers.We hope your calculator will become a faithful companion for your school and professional applications.

    SG49A.book Page 1 Friday, September 16, 2005 1:31 PM

  • Page TOC-1

    Table of Contents

    Chapter 1 - Getting startedBasic Operations, 1-1

    Batteries, 1-1Turning the caAdjusting the Contents of thMenus, 1-3The TOOL meSetting time a

    Introducing the caSelecting calculato

    Operating MoNumber Form

    Standard foFixed formaScientific foEngineeringDecimal co

    Angle MeasurCoordinate Sy

    Selecting CAS settExplanation o

    Selecting Display Selecting the dSelecting propSelecting propSelecting prop

    References, 1-20

    Chapter 2 - IntrCalculator objects

    SG49A.book Page 1 Friday, September 16, 2005 1:31 PMlculator on and off, 1-2display contrast, 1-2e calculators display, 1-3

    nu, 1-3nd date, 1-4lculators keyboard, 1-4r modes, 1-6de, 1-7at and decimal dot or comma, 1-10rmat, 1-10t with decimals, 1-10rmat, 1-11 format, 1-12

    mma vs. decimal point, 1-13e, 1-14stem, 1-14ings, 1-15f CAS settings, 1-16modes, 1-17isplay font, 1-18erties of the line editor, 1-18erties of the Stack, 1-19erties of the equation writer (EQW), 1-20

    oducing the calculator, 2-1

  • Editing expressions in the stack, 2-1Creating arithmetic expressions, 2-1Creating algebraic expressions, 2-4

    Using the Equation Writer (EQW) to create expressions, 2-5Creating arithmetic expressions, 2-5Creating algebraic expressions, 2-7

    Organizing data iThe HOME diSubdirectories

    Variables, 2-9Typing variabCreating varia

    Algebraic mRPN mode,

    Checking variAlgebraic mRPN mode,Using the riListing the c

    Deleting variaUsing functUsing funct

    UNDO and CMD fCHOOSE boxes vsReferences, 2-18

    Chapter 3 - CalExamples of real n

    Using powersReal number funct

    Using calculatHyperbolic fun

    Operations with uThe UNITS me

    SG49A.book Page 2 Friday, September 16, 2005 1:31 PMPage TOC-2

    n the calculator, 2-8rectory, 2-8, 2-9

    le names , 2-9bles, 2-10ode, 2-10

    2-11ables contents, 2-13ode, 2-13

    2-13ght-shift key followed by soft menu key labels, 2-13ontents of all variables in the screen, 2-14bles, 2-14ion PURGE in the stack in Algebraic mode, 2-14ion PURGE in the stack in RPN mode, 2-15unctions, 2-16. Soft MENU, 2-16

    culations with real numbersumber calculations, 3-1

    of 10 in entering data, 3-3ions in the MTH menu, 3-5or menus, 3-5ctions and their inverses, 3-5

    nits, 3-7nu, 3-7

  • Page TOC-3

    Available units, 3-9Attaching units to numbers, 3-9

    Unit prefixes, 3-10Operations with units, 3-11Unit conversions, 3-12

    Physical constants in the calculator, 3-13Defining and usinReference, 3-16

    Chapter 4 - CalDefinitions, 4-1Setting the calcula

    Entering compPolar represen

    Simple operationsThe CMPLX menus

    CMPLX menu CMPLX menu

    Functions applied Function DROITE: Reference, 4-7

    Chapter 5 - AlgEntering algebraicSimple operations

    Functions in thOperations with tr

    Expansion anExpansion an

    Functions in the APolynomials, 5-8

    The HORNERThe variable VThe PCOEF fu

    SG49A.book Page 3 Friday, September 16, 2005 1:31 PMg functions, 3-15

    culations with complex numbers

    tor to COMPLEX mode, 4-1lex numbers, 4-2tation of a complex number, 4-3 with complex numbers, 4-4, 4-4through the MTH menu, 4-4in keyboard, 4-6to complex numbers, 4-6equation of a straight line, 4-7

    ebraic and arithmetic operations objects, 5-1 with algebraic objects, 5-2e ALG menu , 5-3anscendental functions, 5-5d factoring using log-exp functions, 5-5d factoring using trigonometric functions, 5-6RITHMETIC menu, 5-7

    function, 5-8X, 5-8nction, 5-8

  • The PROOT function, 5-9The QUOT and REMAINDER functions, 5-9The PEVAL function , 5-9

    Fractions, 5-9The SIMP2 function, 5-10The PROPFRAC function, 5-10The PARTFRACThe FCOEF fuThe FROOTS

    Step-by-step operReference, 5-12

    Chapter 6 - SolSymbolic solution

    Function ISOLFunction SOLVFunction SOLVFunction ZERO

    Numerical solver Polynomial Eq

    Finding theGenerating6-7Generating

    Financial calcSolving equat

    Function STSolution to simultaReference, 6-11

    Chapter 7 - OpCreating and storiOperations with li

    Changing sign

    SG49A.book Page 4 Friday, September 16, 2005 1:31 PMPage TOC-4

    function, 5-10nction, 5-10function, 5-11ations with polynomials and fractions, 5-11

    ution to equationsof algebraic equations, 6-1, 6-1E, 6-2EVX, 6-4S, 6-4

    menu, 6-5uations, 6-6 solutions to a polynomial equation, 6-6 polynomial coefficients given the polynomial's roots,

    an algebraic expression for the polynomial, 6-8ulations, 6-8ions with one unknown through NUM.SLV, 6-9EQ, 6-9neous equations with MSLV, 6-10

    erations with listsng lists, 7-1sts of numbers, 7-1 , 7-1

  • Page TOC-5

    Addition, subtraction, multiplication, division, 7-2Functions applied to lists, 7-4

    Lists of complex numbers, 7-4Lists of algebraic objects, 7-5The MTH/LIST menu, 7-5The SEQ function, 7-7The MAP function,Reference, 7-7

    Chapter 8 - VecEntering vectors ,

    Typing vectorsStoring vectorUsing the Mat

    Simple operationsChanging sigAddition, subtMultiplicationAbsolute value

    The MTH/VECTORMagnitude, 8Dot product , Cross product

    Reference, 8-8

    Chapter 9 - MaEntering matrices

    Using the MatTyping in the

    Operations with mAddition and Multiplication,


    SG49A.book Page 5 Friday, September 16, 2005 1:31 PM 7-7

    tors8-1 in the stack, 8-1s into variables in the stack, 8-2rix Writer (MTRW) to enter vectors, 8-3 with vectors, 8-5n, 8-5raction, 8-5 by a scalar, and division by a scalar, 8-6 function, 8-6 menu, 8-6-78-7, 8-7

    trices and linear algebrain the stack, 9-1rix Writer, 9-1matrix directly into the stack, 9-2atrices, 9-3

    subtraction, 9-4 9-4on by a scalar, 9-4or multiplication, 9-5

  • Matrix multiplication, 9-5Term-by-term multiplication, 9-6Raising a matrix to a real power, 9-6The identity matrix, 9-7The inverse matrix, 9-7

    Characterizing a matrix (The matrix NORM menu), 9-8Function DET,Function TRAC

    Solution of linear Using the numSolution with tSolution by d

    References, 9-12

    Chapter 10 - GGraphs options inPlotting an expresGenerating a tablFast 3D plots, 10-Reference, 10-7

    Chapter 11 - CaThe CALC (CalculuLimits and derivat

    Function lim, 1Functions DER

    Anti-derivatives aFunctions INT,Definite integr

    Infinite series, 11-Functions TAY

    Reference, 11-6

    SG49A.book Page 6 Friday, September 16, 2005 1:31 PMPage TOC-6

    9-8E, 9-8

    systems, 9-9erical solver for linear systems, 9-9he inverse matrix, 9-11ivision of matrices, 9-11

    raphics the calculator, 10-1sion of the form y = f(x), 10-2e of values for a function, 10-45

    lculus Applicationss) menu, 11-1ives, 11-11-1

    IV and DERVX, 11-3nd integrals, 11-3 INTVX, RISCH, SIGMA and SIGMAVX, 11-3als, 11-45LR, TAYLR0, and SERIES, 11-5

  • Page TOC-7

    Chapter 12 - Multi-variate Calculus ApplicationsPartial derivatives, 12-1Multiple integrals, 12-2Reference, 12-2

    Chapter 13 - Vector Analysis ApplicationsThe del operator, Gradient, 13-1Divergence, 13-2Curl, 13-2Reference, 13-2

    Chapter 14 - DThe CALC/DIFF meSolution to linear

    Function LDECFunction DESOThe variable O

    Laplace TransformLaplace transf

    Fourier series, 14Function FOUFourier series

    Reference, 14-7

    Chapter 15 - PrThe MTH/PROBAB

    Factorials, comRandom numb

    The MTH/PROB mThe Normal dThe Student-t dThe Chi-squarThe F distribut

    SG49A.book Page 7 Friday, September 16, 2005 1:31 PM13-1

    ifferential Equations nu, 14-1

    and non-linear equations, 14-1, 14-1LVE, 14-3DETYPE, 14-3

    s, 14-4orm and inverses in the calculator, 14-4-5RIER, 14-5for a quadratic function, 14-6

    obability DistributionsILITY.. sub-menu - part 1, 15-1binations, and permutations, 15-1

    ers, 15-2enu - part 2, 15-3istribution, 15-3istribution, 15-3

    e distribution, 15-4ion, 15-4

  • Reference, 15-4

    Chapter 16 - Statistical ApplicationsEntering data, 16-1Calculating single-variable statistics, 16-2Sample vs. population, 16-2Obtaining frequenFitting data to a fuObtaining additioConfidence intervaHypothesis testingReference, 16-11

    Chapter 17 - NThe BASE menu, 1Writing non-decimReference, 17-2

    Chapter 18 - UInserting and remFormatting an SD Accessing objects Storing objects onRecalling an objecPurging an objectPurging all objectsSpecifying a direc

    Chapter 19 - EqReference, 19-4

    Limited Warranty,Service, W-3Regulatory informDisposal of Wasteropean Union, W

    SG49A.book Page 8 Friday, September 16, 2005 1:31 PMPage TOC-8

    cy distributions, 16-3nction y = f(x), 16-5

    nal summary statistics, 16-6ls, 16-7, 16-9

    umbers in Different Bases7-1al numbers, 17-2

    sing SD cardsoving an SD card, 18-1card, 18-1on an SD card, 18-2 the SD card, 18-2t from the SD card, 18-3 from the SD card, 18-3 on the SD card (by reformatting), 18-4tory on an SD card, 18-4

    uation Library


    ation, W-5 Equipment by Users in Private Household in the Eu--7

  • Page 1-1

    Chapter 1Getting startedThis chapter provides basic information about the operation of your calculator. It is designed to familiarize you with the basic operations and settings before you perform a calculation.

    Basic Operati

    BatteriesThe calculator uses 4lithium battery for meBefore using the calcfollowing procedure.

    To install the main ba. Make sure the cal

    cover as illustrated

    b. Insert 4 new AAAsure each battery

    To install the backa. Make sure the cal

    to the shown direc

    SG49A.book Page 1 Friday, September 16, 2005 1:31 PMons

    AAA (LR03) batteries as main power and a CR2032 mory backup.ulator, please install the batteries according to the

    atteries culator is OFF. Slide up the battery compartment .

    (LR03) batteries into the main compartment. Make is inserted in the indicated direction.up battery

    culator is OFF. Press down the holder. Push the plate tion and lift it.

  • b. Insert a new CR20facing up.

    c. Replace the plate

    After installing the ba

    Warning: When the lbatteries as soon as pand main batteries at

    Turning the calcThe $ key is locatonce to turn your calshift key @ (first keyfollowed by the $ kin the upper right cor

    Adjusting the dYou can adjust the dithe + or - keys.

    The $(hold) + k

    The $(hold) - kPage 1-2

    32 lithium battery. Make sure its positive (+) side is

    and push it to the original place.

    tteries, press $ to turn the power on.

    ow battery icon is displayed, you need to replace the ossible. However, avoid removing the backup battery the same time to avoid data lost.

    ulator on and offed at the lower left corner of the keyboard. Press it culator on. To turn the calculator off, press the right- in the second row from the bottom of the keyboard), ey. Notice that the $ key has a OFF label printed

    ner as a reminder of the OFF command.

    isplay contrastsplay contrast by holding the $ key while pressing

    ey combination produces a darker display

    ey combination produces a lighter display

  • Page 1-3

    Contents of the calculators displayTurn your calculator on once more. At the top of the display you will have two lines of information that describe the settings of the calculator. The first line shows the characters:

    RAD XYZ HEX R= 'X'

    For details on the meaning of these symbols see Chapter 2 in the calculators users guThe second line show

    indicating that the Hcalculators memory.At the bottom of the d


    associated with the si

    The six labels displadepending on whicassociated with the flabel, and so on.

    MenusThe six labels associamenu of functions. Sdisplay 6 labels at athan six entries. Eachto the next menu pagkey is the third key fro

    The TOOL menuThe soft menu keys fassociated with opesection on variables i

    @EDIT A EDIT theand Chainformat

    @VIEW B VIEW th

    SG49A.book Page 3 Friday, September 16, 2005 1:31 PMide. s the characters

    { HOME }

    OME directory is the current file directory in the

    isplay you will find a number of labels, namely,DIT @VIEW @@RCL@@ @@STO@ !PURGE !CLEARx soft menu keys, F1 through F6:


    yed in the lower part of the screen will change h menu is displayed. But A will always be irst displayed label, B with the second displayed

    ted with the keys A through F form part of a ince the calculator has only six soft menu keys, it only ny point in time. However, a menu can have more group of 6 entries is called a Menu page. To move e (if available), press the L (NeXT menu) key. This m the left in the third row of keys in the keyboard.

    or the default menu, known as the TOOL menu, are rations related to manipulation of variables (see n this Chapter):

    contents of a variable (see Chapter 2 in this guide pter 2 and Appendix L in the users guide for more ion on editing)e contents of a variable

  • These six functions form the first page of the TOOL menu. This menu has actually eight entries arranged in two pages. The second page is available by pressingfrom the left in the thi

    In this case, only thewith them. These com

    Pressing the L keyrecover the TOOL methe second row of key

    Setting time andSee Chapter 1 in the date.

    Introducing thThe figure on the nexwith the numbering ofive functions. The mlabel in the key. Als(9,1), and the ALPHAother keys to activate

    @@RCL@ C ReCaLl the contents of a variable

    @@STO@ D STOre the contents of a variable

    !PURGE E PURGE a variable

    @CLEAR F CLEAR the display or stack


    @HELP B HELP faccalculatoPage 1-4

    the L (NeXT menu) key. This key is the third key rd row of keys in the keyboard.

    first two soft menu keys have commands associated mands are:

    will show the original TOOL menu. Another way to nu is to press the I key (third key from the left in s from the top of the keyboard).

    datecalculators users guide to learn how to set time and

    e calculators keyboardt page shows a diagram of the calculators keyboard f its rows and columns. Each key has three, four, or ain key function correspond to the most prominent

    o, the left-shift key, key (8,1), the right-shift key, key key, key (7,1), can be combined with some of the the alternative functions shown in the keyboard.

    D: CAS CoMmanD, used to launch a command from (Computer Algebraic System) by selecting from a list

    ility describing the commands available in the r

  • Page 1-5

    For example, the Passociated with it:

    P Main Left-sN Righ~p ALPH~p ALPH

    SG49A.book Page 5 Friday, September 16, 2005 1:31 PM key, key(4,4), has the following six functions

    function, to activate the SYMBolic menuhift function, to activate the MTH (Math) menut-shift function, to activate the CATalog functionA function, to enter the upper-case letter PA-Left-Shift function, to enter the lower-case letter p

  • Of the six functions associated with a key only the first four are shown in the keyboard itself. The figure in next page shows these four labels for the P key. Notice that the color and the position of the labels in the key, namely, SYMB, MTH, CAT and P, indicate which is the main function (SYMB), and which of the other three functions is associated with the left-shift (MTH), right-shift (CAT ), and ~ (P) keys.

    For detailed informaAppendix B in the ca

    Selecting calcThis section assumes use of choose and diain the users guide).

    Press the H buttonfrom the top) to show

    Press the !!@@OK#@ soft mselecting different cal

    ~p ALPHA-Right-Shift function, to enter the symbol Page 1-6

    tion on the calculator keyboard operation refer to lculators users guide.

    ulator modesthat you are now at least partially familiar with the log boxes (if you are not, please refer to appendix A

    (second key from the left on the second row of keys the following CALCULATOR MODES input form:

    enu key to return to normal display. Examples of culator modes are shown next.

  • Page 1-7

    Operating ModeThe calculator offers two operating modes: the Algebraic mode, and the Reverse Polish Notation (RPN) mode. The default mode is the Algebraic mode (as indicated in the figure above), however, users of earlier HP calculators may be more familiar with the RPN mode.To select an operating mode, first open the CALCULATOR MODES input form by pressing the H button. The Operating Mode field will be highlighted. Select ththe \ key (second pressing the @CHOOS sodown arrow keys, menu key to completeTo illustrate the diffecalculate the followin

    To enter this expresswriter, O. Pbesides the numeric k



    The equation writermathematical expresfractions, derivatives,writing the expression




    After pressing ` th (3.*(

    Pressing ` again won, if asked, by press

    SG49A.book Page 7 Friday, September 16, 2005 1:31 PMe Algebraic or RPN operating mode by either using from left in the fifth row from the keyboard bottom), or ft menu key. If using the latter approach, use up and , to select the mode, and press the !!@@OK#@ soft

    the operation. rence between these two operating modes we will g expression in both modes:

    ion in the calculator we will first use the equation lease identify the following keys in the keyboard, eypad keys:@.#*+-/R


    is a display mode in which you can build sions using explicit mathematical notation including integrals, roots, etc. To use the equation writer for shown above, use the following keystrokes:R3.*!5.-



    e calculator displays the expression:5.-1/(3.*3.))/23.^3+EXP(2.5))ill provide the following value (accept Approx mode

    ing !!@@OK#@):






  • You could also type the expression directly into the display without using the equation writer, a




    to obtain the same reChange the operatinSelect the RPN operathe @CHOOS soft menu operation. The displa

    Notice that the displato top, as 1, 2, 3, etcdifferent levels are relevel 2, etc.What RPN means is tpressing

    we write the operand

    As you enter the op3` puts the nuthe 3 upwards to occtelling the calculator levels 1 and 2. The r

    SG49A.book Page 8 Friday, September 16, 2005 1:31 PMPage 1-8

    s follows:3.*!5.-



    sult.g mode to RPN by first pressing the H button. ting mode by either using the \ key, or pressing key. Press the @@OK#@ soft menu key to complete the y, for the RPN mode looks as follows:

    y shows several levels of output labeled, from bottom . This is referred to as the stack of the calculator. The ferred to as the stack levels, i.e., stack level 1, stack

    hat, instead of writing an operation such as 3 + 2 by


    s first, in the proper order, and then the operator, i.e.,


    erands, they occupy different stack levels. Entering mber 3 in stack level 1. Next, entering 2 pushes upy stack level 2. Finally, by pressing +, we are to apply the operator, +, to the objects occupying esult, 5, is then placed in level 1.

  • Page 1-9

    Let's try some other simple operations before trying the more complicated expression used earlier for the algebraic operating mode:

    Note the position of texponential operatiolevel 1) before the operation, y (stack lelevel 1) is the root.Try the following exer

    Let's try now the expr

    123/32 123`32/

    42 4`2Q

    3(27) 27R3@



    3` Ente5` Ente3` Ente3* PlacY 1/(3- 5 - 1* 3 23`Ente

    3Q Ente

    / (3 2.5Ente

    ! e2.5,

    SG49A.book Page 9 Friday, September 16, 2005 1:31 PMhe y and x in the last two operations. The base in the n is y (stack level 2) while the exponent is x (stack key Q is pressed. Similarly, in the cubic root vel 2) is the quantity under the root sign, and x (stack

    cise involving 3 factors: (5 + 3) 2

    ession proposed earlier:

    + Calculates (5 +3) first.Completes the calculation.

    r 3 in level 1r 5 in level 1, 3 moves to level 2r 3 in level 1, 5 moves to level 2, 3 to level 3e 3 and multiply, 9 appears in level 13), last value in lev. 1; 5 in level 2; 3 in level 3/(33) , occupies level 1 now; 3 in level 2(5 - 1/(33)), occupies level 1 now.r 23 in level 1, 14.66666 moves to level 2.

    r 3, calculate 233 into level 1. 14.666 in lev. 2.

    (5-1/(33)))/233 into level 1r 2.5 level 1

    goes into level 1, level 2 shows previous value.






  • To select between the ALG vs. RPN operating mode, you can also set/clear system flag 95 through the following keystroke sequence:

    H @FLAGS! 9 `

    Number FormaChanging the numbnumbers are displaextremely useful in opdecimals in a result.To select a number foby pressing the H the option Number fothe standard format, no set decimal placemcalculator (12 significin this guide. To illusexercises:

    Standard formatThis mode is the mosnotation. Press the !!@@Oto return to the calcula(with16 significant figthe maximum 12 sign

    Fixed format withPress the H buttonoption Number formoption Fixed with the

    + (3 (5 - 1/(3 3)))/233 + e2.5 = 12.18369, into lev. 1.

    R ((3 (5 - 1/(33)))/233 + e2.5) = 3.4905156, into 1.

    SG49A.book Page 10 Friday, September 16, 2005 1:31 PMPage 1-10

    t and decimal dot or commaer format allows you to customize the way real yed by the calculator. You will find this feature erations with powers of tens or to limit the number of

    rmat, first open the CALCULATOR MODES input form button. Then, use the down arrow key, , to select rmat. The default value is Std, or Standard format. In the calculator will show floating-point numbers with ent and with the maximum precision allowed by the

    ant digits).To learn more about reals, see Chapter 2 trate this and other number formats try the following

    t used mode as it shows numbers in the most familiar K#@ soft menu key, with the Number format set to Std, tor display. Enter the number 123.4567890123456 ures). Press the ` key. The number is rounded to ificant figures, and is displayed as follows:

    decimals. Next, use the down arrow key, , to select the at. Press the @CHOOS soft menu key, and select the arrow down key .

  • Page 1-11

    Press the right arrowFix. Press the @CHOOSkeys, , select,

    Press the !!@@OK#@ soft m

    Press the !!@@OK#@ soft mnow is shown as:

    Notice how the num123.456789012345as 123.456 because

    Scientific formatTo set this format, staarrow key, , to semenu key, and selec

    SG49A.book Page 11 Friday, September 16, 2005 1:31 PM key, , to highlight the zero in front of the option soft menu key and, using the up and down arrow say, 3 decimals.

    enu key to complete the selection:

    enu key return to the calculator display. The number

    ber is rounded, not truncated. Thus, the number 6, for this setting, is displayed as 123.457, and not the digit after 6 is > 5.

    rt by pressing the H button. Next, use the down lect the option Number format. Press the @CHOOS soft

    t the option Scientific with the arrow down key .

  • Keep the number 3 in front of the Sci. (This number can be changed in the same fashion that we changed the Fixed number of decimals in the example above).

    Press the !!@@OK#@ soft mnow is shown as:

    This result, 1.23E2, i.e., 1.235 102. Infront of the Sci numbsignificant figures afincludes one integer number of significant

    Engineering formaThe engineering formthe powers of ten arethe H button. NexNumber format. PreEngineering with the the Eng. (This numchanged the Fixed nu

    SG49A.book Page 12 Friday, September 16, 2005 1:31 PMPage 1-12

    enu key return to the calculator display. The number

    is the calculators version of powers-of-ten notation, this, so-called, scientific notation, the number 3 in er format (shown earlier) represents the number of ter the decimal point. Scientific notation always figure as shown above. For this case, therefore, the figures is four.

    tat is very similar to the scientific format, except that multiples of three. To set this format, start by pressing t, use the down arrow key, , to select the option ss the @CHOOS soft menu key, and select the option arrow down key . Keep the number 3 in front of ber can be changed in the same fashion that we mber of decimals in an earlier example).

  • Page 1-13

    Press the !!@@OK#@ soft menu key return to the calculator display. The number now is shown as:

    Because this number has three figures in the integer part, it is shown with four significative figEngineering format.

    Decimal comma vDecimal points in flothe user is more famicommas, change the commas, as follows (Std):Press the H button.right arrow key, ,press the soft m

    Press the !!@@OK#@ soft m123.456789012345

    SG49A.book Page 13 Friday, September 16, 2005 1:31 PMures and a zero power of ten, while using the For example, the number 0.00256, will be shown as:

    s. decimal pointating-point numbers can be replaced by commas, if liar with such notation. To replace decimal points for FM option in the CALCULATOR MODES input form to Notice that we have changed the Number Format to

    Next, use the down arrow key, , once, and the highlighting the option __FM,. To select commas, enu key. The input form will look as follows:

    enu key return to the calculator display. The number 6, entered earlier, now is shown as:

  • Angle MeasureTrigonometric functions, for example, require arguments representing plane angles. The calculator provides three different Angle Measure modes for working with angles, namely: Degrees: There are 360 degrees (360) in a complete circumference.

    Radians: There are 2 radians (2 r) in a complete circumference.

    Grades: There areThe angle measure associated functions.To change the angle Press the H butt

    Select the Angle Mfrom left in the fifth@CHOOS soft menu karrow keys, soft menu key to cscreen, the Radian

    Coordinate SysThe coordinate systenumbers are displanumbers and vectorsThere are three coord(RECT), Cylindrical coordinate system: Press the H butt

    Select the Coord Sfrom left in the fifth@CHOOS soft menu karrow keys,

    SG49A.book Page 14 Friday, September 16, 2005 1:31 PMPage 1-14

    400 grades (400 g) in a complete circumference.affects the trig functions like SIN, COS, TAN and

    measure mode, use the following procedure:on. Next, use the down arrow key, , twice. easure mode by either using the \ key (second row from the keyboard bottom), or pressing the

    ey. If using the latter approach, use up and down , to select the preferred mode, and press the !!@@OK#@

    omplete the operation. For example, in the following s mode is selected:

    temm selection affects the way vectors and complex yed and entered. To learn more about complex , see Chapters 4 and 8, respectively, in this guide. inate systems available in the calculator: Rectangular (CYLIN), and Spherical (SPHERE). To change

    on. Next, use the down arrow key, , three times. ystem mode by either using the \ key (second row from the keyboard bottom), or pressing the

    ey. If using the latter approach, use up and down , to select the preferred mode, and press the !!@@OK#@

  • Page 1-15

    soft menu key to complete the operation. For example, in the following screen, the Polar coordinate mode is selected:

    Selecting CASCAS stands for Compof the calculator wfunctions are programadjusted according toCAS settings use the Press the H but

    To change CAS sevalues of the CAS

    To navigate througuse the arrow keys

    To select or deseleunderline before thkey until the right check mark will be

    SG49A.book Page 15 Friday, September 16, 2005 1:31 PM settingsuter Algebraic System. This is the mathematical core here the symbolic mathematical operations and med. The CAS offers a number of settings can be the type of operation of interest. To see the optional

    following:ton to activate the CALCULATOR MODES input form.

    ttings press the @@CAS@@ soft menu key. The default setting are shown below:

    h the many options in the CAS MODES input form, : .ct any of the settings shown above, select the e option of interest, and toggle the soft menu

    setting is achieved. When an option is selected, a shown in the underline (e.g., the Rigorous and Simp

  • Non-Rational options above). Unselected options will show no check mark in the underline preceding the option of interest (e.g., the _Numeric, _Approx, _Complex, _Verbose, _Step/Step, _Incr Pow options above).

    After having selected and unselected all the options that you want in the CAS MODES input form, press the @@@OK@@@ soft menu key. This will take you back to the CALCULATOR MODES input form. To return to normal calculator once more.

    Explanation of Indep var: The ind

    VX = X. Modulo: For opera

    modulus or modulcalculators users

    Numeric: If set, thresult, in calculationumerically.

    Approx: If set, AppIf unchecked, the Cresults in algebrai

    Complex: If set, cothe CAS is in RealSee Chapter 4 for

    Verbose: If set, prooperations.

    Step/Step: If set, poperations. Usefuintegrals, polynomoperations.

    Incr Pow: Increasinshown in increasin

    Rigorous: If set, ca|X| to X.

    Simp Non-Rationaexpressions as mu

    SG49A.book Page 16 Friday, September 16, 2005 1:31 PMPage 1-16

    display at this point, press the @@@OK@@@ soft menu key

    CAS settingsependent variable for CAS applications. Typically,

    tions in modular arithmetic this variable holds the o of the arithmetic ring (see Chapter 5 in the guide).e calculator produces a numeric, or floating-point ns. Note that constants will always be evaluated

    roximate mode uses numerical results in calculations. AS is in Exact mode, which produces symbolic

    c calculations.mplex number operations are active. If unchecked

    mode, i.e., real number calculations are the default. operations with complex numbers.vides detailed information in certain CAS

    rovides step-by-step results for certain CAS l to see intermediate steps in summations, derivatives, ial operations (e.g., synthetic division), and matrix

    g Power, means that, if set, polynomial terms are g order of the powers of the independent variable.lculator does not simplify the absolute value function

    l: If set, the calculator will try to simplify non-rational ch as possible.

  • Page 1-17

    Selecting Display modesThe calculator display can be customized to your preference by selecting different display modes. To see the optional display settings use the following: First, press the H button to activate the CALCULATOR MODES input

    form. Within the CALCULATOR MODES input form, press the @@DISP@ soft menu key to d

    To navigate througform, use the arrow

    To select or deselecheck mark, selectoggle the When an option iunderline (e.g., thUnselected optionthe option of interin the Edit: line ab

    To select the Font option in the DISP

    After having selecthe DISPLAY MODtake you back to tnormal calculator once more.

    SG49A.book Page 17 Friday, September 16, 2005 1:31 PMisplay the DISPLAY MODES input form.

    h the many options in the DISPLAY MODES input keys: .

    ct any of the settings shown above, that require a t the underline before the option of interest, and soft menu key until the right setting is achieved. s selected, a check mark will be shown in the e Textbook option in the Stack: line above). s will show no check mark in the underline preceding est (e.g., the _Small, _Full page, and _Indent options ove).for the display, highlight the field in front of the Font: LAY MODES input form, and use the @CHOOS soft menu.ted and unselected all the options that you want in ES input form, press the @@@OK@@@ soft menu key. This will he CALCULATOR MODES input form. To return to display at this point, press the @@@OK@@@ soft menu key

  • Selecting the display fontFirst, press the H button to activate the CALCULATOR MODES input form. Within the CALCULATOR MODES input form, press the @@DISP@ soft menu key to display the DISPLAY MODES input form. The Font: field is highlighted, and the option Ft8_0: system 8 is selected. This is the default value of the display font. Pressing the @CHOOS soft menu key will provide a list of available system fonts, as shown below:

    The options availableand a Browse.. optmemory for additioninto the calculator.Practice changing thmenu key to effect ththe @@@OK@@@ soft menu form. To return to nosoft menu key onceaccommodate the dif

    Selecting propeFirst, press the H form. Within the CAmenu key to displayarrow key, , onproperties that can (checked) the followin

    Instructions on the useusers guide.

    _Small Chan_Full page Allow_Indent Auto

    SG49A.book Page 18 Friday, September 16, 2005 1:31 PMPage 1-18

    are three standard System Fonts (sizes 8, 7, and 6) ion. The latter will let you browse the calculator al fonts that you may have created or downloaded

    e display fonts to sizes 7 and 6. Press the OK soft e selection. When done with a font selection, press key to go back to the CALCULATOR MODES input rmal calculator display at this point, press the @@@OK@@@ more and see how the stack display change to ferent font.

    rties of the line editorbutton to activate the CALCULATOR MODES input LCULATOR MODES input form, press the @@DISP@ soft the DISPLAY MODES input form. Press the down

    ce, to get to the Edit line. This line shows three be modified. When these properties are selected g effects are activated:

    of the line editor are presented in Chapter 2 in the

    ges font size to smalls to place the cursor after the end of the line

    indent cursor when entering a carriage return

  • Page 1-19

    Selecting properties of the StackFirst, press the H button to activate the CALCULATOR MODES input form. Within the CALCULATOR MODES input form, press the @@DISP@ soft menu key (D) to display the DISPLAY MODES input form. Press the down arrow key, , twice, to get to the Stack line. This line shows two properties that can be modified. When these properties are selected (checked) the following effects are activated:

    To illustrate these seequation writer to typ


    In Algebraic mode, thwith neither _Small n

    With the _Small optio

    With the _Textbook othe _Small option is s

    _Small Chaninforoverr

    _Textbook Dispmath

    SG49A.book Page 19 Friday, September 16, 2005 1:31 PMttings, either in algebraic or RPN mode, use the e the following definite integral:0\xx`

    e following screen shows the result of these keystrokes or _Textbook are selected:

    n selected only, the display looks as shown below:

    ption selected (default value), regardless of whether elected or not, the display shows the following result:

    ges font size to small. This maximizes the amount of mation displayed on the screen. Note, this selection ides the font selection for the stack display.lays mathematical expressions in graphical ematical notation

  • Selecting properties of the equation writer (EQW)First, press the H button to activate the CALCULATOR MODES input form. Within the CALCULATOR MODES input form, press the @@DISP@ soft menu key to display the DISPLAY MODES input form. Press the down arrow key, , three times, to get to the EQW (Equation Writer) line. This line shows two properties that can be modified. When these properties are selected (checked) the following effects are activated:

    Detailed instructions presented elsewhere

    For the example of th

    _Small Stack Disp inproduces the followin

    ReferencesAdditional referencesin Chapter 1 and Ap

    _Small Ce

    _Small Stack Disp Se

    SG49A.book Page 20 Friday, September 16, 2005 1:31 PMPage 1-20

    on the use of the equation editor (EQW) are in this manual.

    e integral , presented above, selecting the

    the EQW line of the DISPLAY MODES input form g display:

    on the subjects covered in this Chapter can be found pendix C of the calculators users guide.

    hanges font size to small while using the equation ditorhows small font in the stack after using the equation ditor



  • Page 2-1

    Chapter 2Introducing the calculatorIn this chapter we present a number of basic operations of the calculator including the use of the Equation Writer and the manipulation of data objects in the calculator. Study the examples in this chapter to get a good grasp of the capabilities of the calculator for future applications.

    Calculator obSome of the most comwith a decimal poinwritten without a dnumbers (written as objects are described

    Editing expreIn this section we precalculator display or

    Creating arithmFor this example, we format with 3 decimarithmetic expression

    To enter this expressio5.*

    The resulting expressiPress ` to get the

    SG49A.book Page 1 Friday, September 16, 2005 1:31 PMjectsmonly used objects are: reals (real numbers, written

    t, e.g., -0.0023, 3.56), integers (integer numbers, ecimal point, e.g., 1232, -123212123), complex an ordered pair, e.g., (3,-2)), lists, etc. Calculator in Chapters 2 and 24 in the calculators user guide.

    ssions in the stacksent examples of expression editing directly into the stack.

    etic expressionsselect the Algebraic operating mode and select a Fixals for the display. We are going to enter the


    n use the following keystrokes:1.+1/7.5/


    on is: 5*(1+1/7.5)/( 3-2^3). expression in the display as follows:






  • Notice that, if your CAS is set to EXACT (see Appendix C in users guide) and you enter your ethe result is a symboli


    Before producing a rmode. Accept the chmode with three deci

    In this case, when theas you press `, thexpression. If the ecalculator will reprod


    The result will be show

    To evaluate the expre

    SG49A.book Page 2 Friday, September 16, 2005 1:31 PMPage 2-2

    xpression using integer numbers for integer values, c quantity, e.g.,1+1/7.5/


    esult, you will be asked to change to Approximate ange to get the following result (shown in Fix decimal mal places see Chapter 1):

    expression is entered directly into the stack, as soon e calculator will attempt to calculate a value for the xpression is preceded by a tickmark, however, the uce the expression as entered. For example:



    n as follows:

    ssion we can use the EVAL function, as follows:


  • Page 2-3

    If the CAS is set to Exact, you will be asked to approve changing the CAS setting to Approx. Once this is done, you will get the same result as before.An alternative way to evaluate the expression entered earlier between quotes is by using the option .We will now enter the expression used above when the calculator is set to the RPN operating mode. We also set the CAS to Exact, the display to Textbook, and the nuexpression between q


    Resulting in the outpu

    Press ` once morestack for evaluation.

    This expression is secomponents to the re[using ] and evaluThis latter result is palthough representingthey are not, we subtfunction EVAL: -For additional informor stack, see Chapter

    SG49A.book Page 3 Friday, September 16, 2005 1:31 PMmber format to Standard. The keystrokes to enter the uotes are the same used earlier, i.e.,




    to keep two copies of the expression available in the We first evaluate the expression by pressing:

    !` or @`mi-symbolic in the sense that there are floating-point sult, as well as a 3. Next, we switch stack locations ate using function NUM, i.e., .

    urely numerical, so that the two results in the stack, the same expression, seem different. To verify that

    ract the two values and evaluate this difference using . The result is zero (0.).

    ation on editing arithmetic expressions in the display 2 in the calculators users guide.

  • Creating algebraic expressionsAlgebraic expressions include not only numbers, but also variable names. As an example, we will enter the following algebraic expression:

    We set the calculatorthe display to Textbofollowing keystrokes:



    Press ` to get the f

    Entering this expressexactly the same as thFor additional inforcalculators display o






    SG49A.book Page 4 Friday, September 16, 2005 1:31 PMPage 2-4

    operating mode to Algebraic, the CAS to Exact, and ok. To enter this algebraic expression we use the




    ollowing result:

    ion when the calculator is set in the RPN mode is is Algebraic mode exercise.mation on editing algebraic expressions in the r stack see Chapter 2 in the calculators users guide.

    byR +

  • Page 2-5

    Using the Equation Writer (EQW) to create expressionsThe equation writer is an extremely powerful tool that not only let you enter or see an equation, but also allows you to modify and work/apply functions on all or part of the equation.The Equation Writer is launched by pressing the keystroke combination O (the third keresulting screen is the

    The six soft menu keCURS, BIG, EVAL, information on these users guide.

    Creating arithmEntering arithmetic eentering an arithmetmain difference is thawritten in textbook following keystrokes iThe result is the expre

    The cursor is shown edition location. Foabove, type now:


    The edited expression

    SG49A.book Page 5 Friday, September 16, 2005 1:31 PMy in the fourth row from the top in the keyboard). The following. Press L to see the second menu page:

    ys for the Equation Writer activate functions EDIT, FACTOR, SIMPLIFY, CMDS, and HELP. Detailed functions is provided in Chapter 3 of the calculators

    etic expressionsxpressions in the Equation Writer is very similar to ic expression in the stack enclosed in quotes. The t in the Equation Writer the expressions produced are style instead of a line-entry style. For example, try the n the Equation Writer screen: 5/5+2ssion:

    as a left-facing key. The cursor indicates the current r example, for the cursor in the location indicated


    looks as follows:

  • Suppose that you want to replace the quantity between parentheses in the denominator (i.e., 5+() delete the currewith 2/2, as follows

    When hit this point th

    In order to insert the dthe entire 2 expressionce. At that point, w

    The expression now lo

    Suppose that now expression, i.e., you w

    SG49A.book Page 6 Friday, September 16, 2005 1:31 PMPage 2-6

    1/3) with (5+2/2). First, we use the delete key nt 1/3 expression, and then we replace that fraction


    e screen looks as follows:

    enominator 2 in the expression, we need to highlight on. We do this by pressing the right arrow key () e enter the following keystrokes:


    oks as follows:

    you want to add the fraction 1/3 to this entire ant to enter the expression:








  • Page 2-7

    First, we need to highlight the entire first term by using either the right arrow () or the upper arrow () keys, repeatedly, until the entire expression is highlighted, i.e., seven times, producing:

    Once the expression3 to add the fracti

    Creating algebrAn algebraic expressthat English and Grean algebraic exprescreating an arithmekeyboard is included.To illustrate the use owe will use the folloexpression:

    Use the following key2/R3


    NOTE: Alternativeright of the 2 in thcombination

    SG49A.book Page 7 Friday, September 16, 2005 1:31 PM is highlighted as shown above, type +1/on 1/3. Resulting in:

    aic expressionsion is very similar to an arithmetic expression, except ek letters may be included. The process of creating sion, therefore, follows the same idea as that of tic expression, except that use of the alphabetic f the Equation Writer to enter an algebraic equation wing example. Suppose that we want to enter the



    ly, from the original position of the cursor (to the e denominator of 2/2), we can use the keystroke

    , interpreted as ( ).







  • ~y/~tQ1/3

    This results in the output:

    In this example we(~x), severacombination of (~c~yletter, you need to usewant to enter. Also, CHARS menu (combination that prokeystroke combinationFor additional infosimplifying algebraicguide.

    Organizing dYou can organize ddirectory tree. The bdirectory described n

    The HOME direTo get to the HOME das needed -- until thedisplay header. AlteHOME directory contthe variables in the so

    SG49A.book Page 8 Friday, September 16, 2005 1:31 PMPage 2-8

    used several lower-case English letters, e.g., x l Greek letters, e.g., (~n), and even a Greek and English letters, namely, y). Keep in mind that to enter a lower-case English

    the combination: ~ followed by the letter you you can always copy special characters by using the

    ) if you dont want to memorize the keystroke duces it. A listing of commonly used ~s is listed in Appendix D of the users guide.rmation on editing, evaluating, factoring, and expressions see Chapter 2 of the calculators users

    ata in the calculatorata in your calculator by storing variables in a asis of the calculators directory tree is the HOME


    ctoryirectory, press the UPDIR function () -- repeat {HOME} spec is shown in the second line of the

    rnatively, use (hold) . For this example, the ains nothing but the CASDIR. Pressing J will show ft menu keys:

  • Page 2-9

    SubdirectoriesTo store your data in a well organized directory tree you may want to create subdirectories under the HOME directory, and more subdirectories within subdirectories, in a hierarchy of directories similar to folders in modern computers. The subdirectories will be given names that may reflect the contents of each subdirectory, or any arbitrary name that you can think off. For details on manipulation of directories see Chapter 2 in the calculators users gu

    VariablesVariables are similar store one object (numatrices, programs, ecan be any combinawith a letter (either Esuch as the arrow (an alphabetical charanot. Valid examplesAB12, A12, VelA variable can not hSome of the reservALRMDAT, CST, EQPRTPAR, VPAR, ZPAR,Variables can be orcalculators users gu

    Typing variableTo name variables, ymay or may not be cyou can lock the alph~~ locks the athis fashion, pressingletter, while pressing character. If the alphlock it in lower case, ~~~ loclocked in this fashionupper case letter. To

    SG49A.book Page 9 Friday, September 16, 2005 1:31 PMide.

    to files on a computer hard drive. One variable can merical values, algebraic expressions, lists, vectors, tc). Variables are referred to by their names, which

    tion of alphabetic and numerical characters, starting nglish or Greek). Some non-alphabetic characters, ) can be used in a variable name, if combined with cter. Thus, A is a valid variable name, but is

    of variable names are: A, B, a, b, , , A1, , Z0, z1, etc.ave the same name as a function of the calculator. ed calculator variable names are the following: , EXPR, IERR, IOPAR, MAXR, MINR, PICT, PPAR, der_, e, i, n1,n2, , s1, s2, , DAT, PAR, , .ganized into sub-directories (see Chapter 2 in the ide).

    names ou will have to type strings of letters at once, which ombined with numbers. To type strings of characters abetic keyboard as follows:lphabetic keyboard in upper case. When locked in the before a letter key produces a lower case the key before a letter key produces a special abetic keyboard is already locked in upper case, to type, ~.ks the alphabetic keyboard in lower case. When , pressing the before a letter key produces an

    unlock lower case, press ~.

  • To unlock the upper-case locked keyboard, press ~.Try the following exercises:




    The calculator display will show the following (left-hand side is Algebraic mode, right-hand side

    Creating variabThe simplest way to cexamples are used toJ if needed to see

    Algebraic modeTo store the value of~a. AT this p

    Press ` to create menu key labels when



    SG49A.book Page 10 Friday, September 16, 2005 1:31 PMPage 2-10

    is RPN mode):

    lesreate a variable is by using the K. The following store the variables listed in the following table (Press variables menu):

    0.25 into variable : 0.25\K oint, the screen will look as follows:

    the variable. The variable is now shown in the soft you press J:

    Contents Type-0.25 real

    3105 realr/(m+r)' algebraic[3,2,1] vector3+5i complex program

  • Page 2-11

    The following are the keystrokes for entering the remaining variables:

    A12: 3V5K~a12`

    Q: ~r/


    R: 3

    z1: 3+5*Complex mode if ask

    p1: ~


    The screen, at this po

    You will see six of thp1, z1, R, Q, A12, a

    RPN mode(Use H\@@OK@@ toto store the value o~a`. At t

    With 0.25 on the leyou can use the K in the soft menu key l



    K~z1` (Accept change toed).



    int, will look as follows:

    e seven variables listed at the bottom of the screen:.

    change to RPN mode). Use the following keystrokesf 0.25 into variable : .25\`his point, the screen will look as follows:

    vel 2 of the stack and '' on the level 1 of the stack,key to create the variable. The variable is now shownabels when you press J:

  • To enter the value 3105 into A12, we can use a shorter version of the procedure: 3V5~a12`KHere is a way to enter the contents of Q:Q: ~r/ ~m+~

    To enter the value procedure:R: 3#2Notice that to separathe space key (#)Algebraic mode. z1: 3+5p1: ~rQ2

    The screen, at this po

    You will see six of thp1, z1, R, Q, A12,

    SG49A.book Page 12 Friday, September 16, 2005 1:31 PMPage 2-12


    of R, we can use an even shorter version of the

    #1 ~rK

    te the elements of a vector in RPN mode we can use , rather than the comma () used above in



    ~p1`K.int, will look as follows:

    e seven variables listed at the bottom of the screen: .

  • Page 2-13

    Checking variables contentsThe simplest way to check a variable content is by pressing the soft menu key label for the variable. For example, for the variables listed above, press the following keys to see the contents of the variables:

    Algebraic modeType these keystrokes: J@@z1@@ ` @@@R@@ `@@@Q@@@ `. At this point, the screen looks as follow

    RPN modeIn RPN mode, you olabel to get the conteunder consideration, , created above, as At this point, the scre

    Using the right-shIn Algebraic mode, yJ@ and then texamples:


    NOTE: In RPN modthe corresponding s

    SG49A.book Page 13 Friday, September 16, 2005 1:31 PMs:

    nly need to press the corresponding soft menu key nts of a numerical or algebraic variable. For the case we can try peeking into the variables z1, R, Q, A12, follows: J@@z1@@ @@@R@@ @@@Q@@ @@A12@@ @@@@ en looks like this:

    ift key followed by soft menu key labelsou can display the content of a variable by pressing he corresponding soft menu key. Try the following

    @p1@@ @@z1@@ @@@R@@ @@@Q@@ @@A12@@

    e, you dont need to press @ (just J and then oft menu key.)

  • This produces the following screen (Algebraic mode in the left, RPN in the right)

    Notice that this time tsee the remaining var

    Listing the contentUse the keystroke comin the screen. For exa

    Press $ to return to

    Deleting variabThe simplest way of function can be acceusing the FILES menu

    Using function PUOur variable list concommand PURGE to The screen will now s

    SG49A.book Page 14 Friday, September 16, 2005 1:31 PMPage 2-14

    he contents of program p1 are listed in the screen. To iables in this directory, press L.

    s of all variables in the screenbination to list the contents of all variables mple:

    normal calculator display.

    lesdeleting variables is by using function PURGE. This ssed directly by using the TOOLS menu (I), or by @@OK@@ .

    RGE in the stack in Algebraic modetains variables p1, z1, Q, R, and . We will use delete variable p1. Press I @PURGE@ J @@p1@@ `. how variable p1 removed:

  • Page 2-15

    You can use the PURGE command to erase more than one variable by placing their names in a list in the argument of PURGE. For example, if now we wanted to purge variables R and Q, simultaneously, we can try the following exercise. Press :

    I @PURGE@ J @@@R!@@ J @@@Q!@@At this point, the screen will show the following command ready to be executed:

    To finish deleting theremaining variables:

    Using function PUAssuming that our vaWe will use commanI @PURGE@. The scre

    To delete two variabla list (in RPN mode,commas as in Algeb


    Then, press I@PURGAdditional informatioof the calculators use

    SG49A.book Page 15 Friday, September 16, 2005 1:31 PM variables, press `. The screen will now show the

    RGE in the stack in RPN moderiable list contains the variables p1, z1, Q, R, and . d PURGE to delete variable p1. Press @@p1@@ ` en will now show variable p1 removed:

    es simultaneously, say variables R and Q, first create the elements of the list need not be separated by raic mode): @@@R!@@ @@@Q!@@ `

    E@ use to purge the variables.n on variable manipulation is available in Chapter 2 rs guide.

  • UNDO and CMD functionsFunctions UNDO and CMD are useful for recovering recent commands, or to revert an operation if a mistake was made. These functions are associated with the HIST key: UNDO results from the keystroke sequence , while CMD results from the keystroke sequence .

    CHOOSE boxes vs. Soft MENUIn some of the exercisof commands displayCHOOSE boxes. Heboxes to Soft MENUsAlthough not appliedtwo options for menusIn this exercise, we udirectory. The steps a



    SG49A.book Page 16 Friday, September 16, 2005 1:31 PMPage 2-16

    es presented in this chapter we have seen menu lists ed in the screen. These menu lists are referred to as rein we indicate the way to change from CHOOSE , and vice versa, through an exercise. to a specific example, the present exercise shows the in the calculator (CHOOSE boxes and soft MENUs). se the ORDER command to reorder variables in a

    re shown for Algebraic mode.

    Show PROG menu list and select MEMORY

    Show the MEMORY menu list and select DIRECTORY

    Show the DIRECTORY menu list and select ORDER

  • Page 2-17

    There is an alternativsetting system flag 11in the calculators use


    The screen shows flag

    Press the soft will reflect that chang

    Press @@OK@@ twice to reNow, well try to finthose used above, i.emenu list, we get sofmenu, i.e.,


    SG49A.book Page 17 Friday, September 16, 2005 1:31 PMe way to access these menus as soft MENU keys, by 7. (For information on Flags see Chapters 2 and 24 rs guide). To set this flag try the following:@FLAGS!

    117 not set (CHOOSE boxes), as shown here:

    menu key to set flag 117 to soft MENU. The screen e:

    turn to normal calculator display.d the ORDER command using similar keystrokes to ., we start with . Notice that instead of a

    t menu labels with the different options in the PROG

    activate the ORDER command

  • Press B to select the MEMORY soft menu ()@@MEM@@). The display now shows:

    Press E to select th

    The ORDER commandkey to find it:

    To activate the ORDE

    ReferencesFor additional informadisplay or in the Equguide. For CAS (Comthe calculators usersthe calculators users

    NOTE: most of thcurrent setting of flahave set the flag buyou should clear the

    SG49A.book Page 18 Friday, September 16, 2005 1:31 PMPage 2-18

    e DIRECTORY soft menu ()@@DIR@@)

    is not shown in this screen. To find it we use the L

    R command we press the C(@ORDER) soft menu key.

    tion on entering and manipulating expressions in the ation Writer see Chapter 2 of the calculators users puter Algebraic System) settings, see Appendix C in

    guide. For information on Flags see, Chapter 24 in guide.

    e examples in this user manual assume that the g 117 is its default setting (that is, not set). If you t want to strictly follow the examples in this manual, flag before continuing.

  • Page 3-1

    Chapter 3Calculations with real numbersThis chapter demonstrates the use of the calculator for operations and functions related to real numbers. The user should be acquainted with the keyboard to identify certain functions available in the keyboard (e.g., SIN, COS, TAN, etc.). Also, it is assumed that the reader knows how to change the calculators operboxes (Chapter 1), a

    Examples of rTo perform real numbReal (as opposed to most operations. Themode.Some operations with Use the \ key f

    For example, in AIn RPN mode, e.g

    Use the Ykey toFor example, in AIn RPN mode use

    For addition, subtroperation key, namExamples in ALG





    Examples in RPN 3




    Alternatively, in RPspace (#) befor


    SG49A.book Page 1 Friday, September 16, 2005 1:31 PMating system (Chapter 1), use menus and choose nd operate with variables (Chapter 2).

    eal number calculationser calculations it is preferred to have the CAS set to

    Complex) mode. Exact mode is the default mode for refore, you may want to start your calculations in this

    real numbers are illustrated next:or changing sign of a number. LG mode, \2.5`. ., 2.5\. calculate the inverse of a number.

    LG mode, Y2`. 4Y.action, multiplication, division, use the proper ely, +-*/.





    mode:.7` 5.2+.3` 8.5-

    .2` 2.5*

    .3` 4.5/

    N mode, you can separate the operands with a e pressing the operator key. Examples:


  • 6.3#8.5-



    Parentheses () can be used to group operations, as well as to enclose arguments of functions. In ALG mode:


    In RPN mode, youdirectly on the stac


    In RPN mode, typiyou to enter the ex

    For both, ALG andO5+

    The expression ca

    The absolute valueExample in ALG m

    Example in RPN m

    The square functioExample in ALG m

    Example in RPN m

    The square root fucalculating in the argument, e.g.,

    In RPN mode, ente

    SG49A.book Page 2 Friday, September 16, 2005 1:31 PMPage 3-2


    do not need the parenthesis, calculation is done k:.2+7`2.2-/

    ng the expression between single quotes will allow pression like in algebraic mode:



    RPN modes, using the Equation Writer:3.2/7-2.2

    n be evaluated within the Equation writer, by using @EVAL@ or, @EVAL@ function, ABS, is available through . ode:



    n, SQ, is available through . ode:\2.3`


    nction, , is available through the R key. When stack in ALG mode, enter the function before the


    r the number first, then the function, e.g., 123.4R

  • Page 3-3

    The power function, ^, is available through the Q key. When calculating in the stack in ALG mode, enter the base (y) followed by the Q key, and then the exponent (x), e.g.,


    In RPN mode, enter the number first, then the function, e.g.,5.2`1.25Q

    The root function, XROOT(y,x), is available through the keystroke combination enter the function by commas, e.g.,

    In RPN mode, entefunction call, e.g.,

    Logarithms of bas (functionantilogarithm) is cfunction is entered

    In RPN mode, the

    Using powers oPowers of ten, i.e., nusing the V key. F


    Or, in RPN mode:4

    Natural logarithmthe exponential fumode, the function

    In RPN mode, the

    SG49A.book Page 3 Friday, September 16, 2005 1:31 PM. When calculating in the stack in ALG mode, XROOT followed by the arguments (y,x), separated


    r the argument y, first, then, x, and finally the


    e 10 are calculated by the keystroke combination LOG) while its inverse function (ALOG, or alculated by using . In ALG mode, the before the argument:2.45`


    argument is entered before the function2.45


    f 10 in entering dataumbers of the form -4.5 10-2, etc., are entered by or example, in ALG mode:



    s are calculated by using (function LN) while nction (EXP) is calculated by using . In ALG is entered before the argument:2.45`


    argument is entered before the function

  • 2.45`


    Three trigonometric functions are readily available in the keyboard: sine (S), cosine (T), and tangent (U). Arguments of these functions are angles in either degrees, radians, grades. The following examples use angles in degrees (DEG): In ALG mode:

    In RPN mode:

    The inverse trigonoarcsine ()The answer from tmeasure (DEG, RAIn ALG mode:

    In RPN mode:

    All the functions descALOG, LN, EXP, SIN,with the fundamental expressions. The EChapter 2, is idealcalculator operation m

    SG49A.book Page 4 Friday, September 16, 2005 1:31 PMPage 3-4







    metric functions available in the keyboard are the , arccosine (), and arctangent (). hese functions will be given in the selected angular D, GRD). Some examples are shown next:







    ribed above, namely, ABS, SQ, , ^, XROOT, LOG, COS, TAN, ASIN, ACOS, ATAN, can be combined operations (+-*/) to form more complex quation Writer, whose operations is described in for building such expressions, regardless of the ode.

  • Page 3-5

    Real number functions in the MTH menuThe MTH () menu include a number of mathematical functions mostly applicable to real numbers. With the default setting of CHOOSE boxes for system flag 117 (see Chapter 2), the MTH menu shows the following functions:

    The functions are gro3. lists, 7. probability,5. real, 6. base, 8. constants available inIn general, be awarefor each function, anfirst the function andshould enter the argu

    Using calculato1. We will describe i

    section with the incalculator menus. different options.

    2. To quickly select oCHOOSE box), siFor example, to sesimply press 4.

    Hyperbolic funcSelecting Option 4. Hproduces the hyperbo

    SG49A.book Page 5 Friday, September 16, 2005 1:31 PM uped by th type of argument (1. vectors, 2. matrices, 9. complex) or by the type of function (4. hyperbolic, fft). It also contains an entry for the mathematical the calculator, entry 10. of the number and order of the arguments required d keep in mind that, in ALG mode you should select then enter the argument, while in RPN mode, you ment in the stack first, and then select the function.

    r menusn detail the use of the 4. HYPERBOLIC.. menu in this tention of describing the general operation of Pay close attention to the process for selecting

    ne of the numbered options in a menu list (or mply press the number for the option in the keyboard. lect option 4. HYPERBOLIC.. in the MTH menu,

    tions and their inversesYPERBOLIC.. , in the MTH menu, and pressing @@OK@@, lic function menu:

  • For example, in ALGtanh(2.5), is the follow

    In the RPN mode, following:


    The operations shownfor system flag 117 (this flag (see Chaptefollows (left-hand side

    Pressing L shows t

    Thus, to select, for exformat press )@@HYP@ , to

    SG49A.book Page 6 Friday, September 16, 2005 1:31 PMPage 3-6

    mode, the keystroke sequence to calculate, say, ing:4@@OK@@ 5@@OK@@ 2.5`

    the keystrokes to perform this calculation are the

    5`4@@OK@@ 5@@OK@@

    above assume that you are using the default setting CHOOSE boxes). If you have changed the setting of r 2) to SOFT menu, the MTH menu will show as in ALG mode, right hand side in RPN mode):

    he remaining options:

    ample, the hyperbolic functions menu, with this menu produce:

  • Page 3-7

    Finally, in order to select, for example, the hyperbolic tangent (tanh) function, simply press @@TANH@.

    For example, to calculate tanh(2.5), in the ALG mode, when using SOFT menus over CHOOSE boxes, follow this procedure:

    In RPN mode, the sam2

    As an exercise of apvalues:

    Operations wNumbers in the calcupossible to calculateproduce a result with

    The UNITS menThe units menu (associated CHOOSE boxes, the

    NOTE: To see additional options in these soft menus, press the Lkey or the keystroke sequence.

    SINH (2.5) =COSH (2.5)TANH(2.5) =EXPM(2.0) =

    SG49A.book Page 7 Friday, September 16, 2005 1:31 PM@@HYP@ @@TANH@ 2.5`

    e value is calculated using:.5` )@@HYP@ @@TANH@

    plications of hyperbolic functions, verify the following

    ith unitslator can have units associated with them. Thus, it is results involving a consistent system of units and the appropriate combination of units.

    uis launched by the keystroke combination

    with the 6 key). With system flag 117 set to result is the following menu:

    6.05020.. ASINH(2.0) = 1.4436 = 6.13228.. ACOSH (2.0) = 1.3169 0.98661.. ATANH(0.2) = 0.2027 6.38905. LNP1(1.0) = 0.69314.

  • Option 1. Tools.. conlater). Options 2. Lenumber of units forselecting option 8. Fo

    The user will recognizvery often nowadays)dynes, gf = grams fa unit of mass), kip =distinguish from pounTo attach a unit objeunderscore. Thus, a fFor extensive operatioway of attaching unChapter 2), and usfollowing menus. Pre

    SG49A.book Page 8 Friday, September 16, 2005 1:31 PMPage 3-8

    tains functions used to operate on units (discussed ngth.. through 17.Viscosity.. contain menus with a

    each of the quantities described. For example, rce.. shows the following units menu:

    e most of these units (some, e.g., dyne, are not used from his or her physics classes: N = newtons, dyn = orce (to distinguish from gram-mass, or plainly gram, kilo-poundal (1000 pounds), lbf = pound-force (to

    d-mass), pdl = poundal.ct to a number, the number must be followed by an orce of 5 N will be entered as 5_N.ns with units SOFT menus provide a more convenient its. Change system flag 117 to SOFT menus (see e the keystroke combination to get the ss L to move to the next menu page.

  • Page 3-9

    Pressing on the appropriate soft menu key will open the sub-menu of units for that particular selection. For example, for the @)SPEED sub-menu, the following units are available:

    Pressing the soft menuRecall that you can a, e.g., for the

    Available unitsFor a complete list ousers guide.

    Attaching unitsTo attach a unit objeunderscore (5_N. Here is the sequenceflag 117 set to CHOO


    To enter this same qfollowing keystrokes:

    NOTE: Use the navigate through th

    NOTE: If you forgewhere N here repre

    SG49A.book Page 9 Friday, September 16, 2005 1:31 PM key @)UNITS will take you back to the UNITS menu.lways list the full menu labels in the screen by using @)ENRG set of units the following labels will be listed:

    f available units see Chapter 3 in the calculators

    to numbersct to a number, the number must be followed by an , key(8,5)). Thus, a force of 5 N will be entered as

    of steps to enter this number in ALG mode, system SE boxes:

    8@@OK@@ @@OK@@ `

    uantity, with the calculator in RPN mode, use the

    L key or the keystroke sequence to e menus.

    t the underscore, the result is the expression 5*N, sents a possible variable name and not Newtons.

  • 58@@OK@@ @@OK@@

    Notice that the underscore is entered automatically when the RPN mode is active.The keystroke sequences to enter units when the SOFT menu option is selected, in both ALG and RPN modes, are illustrated next. For example, in ALG mode, to enter the quantity 5_N use:

    5L @)@FORCE @@@N@@ `

    The same quantity, en

    Unit prefixesYou can enter prefixefrom the SI system. Tname, and by the eprefix:

    (*) In the SI system, tcalculator, however.To enter these prefixeexample, to enter 123

    NOTE: You can enunits with the ~kentry: 5_N

    Prefix NameY yottaZ zettaE exaP petaT teraG gigaM megak,K kiloh,H hectoD(*) deka

    SG49A.book Page 10 Friday, September 16, 2005 1:31 PMPage 3-10

    tered in RPN mode uses the following keystrokes:5L @)@FORCE @@@N@@

    s for units according to the following table of prefixes he prefix abbreviation is shown first, followed by its

    xponent x in the factor 10x corresponding to each

    his prefix is da rather than D. Use D for deka in the

    s, simply type the prefix using the ~ keyboard. For pm (picometer), use:

    ter a quantity with units by typing the underline and eyboard, e.g., 5~n will produce the

    x Prefix Name x+24 d deci -1+21 c centi -2+18 m milli -3+15 micro -6+12 n nano -9+9 p pico -12+6 f femto -15+3 a atto -18+2 z zepto -21+1 y yocto -24

  • Page 3-11


    Using UBASE (type the name) to convert to the default unit (1 m) results in:

    Operations withHere are some calcuwarned that, when menclosed each quantifor example, the (12.5_m)*(5.2_yd) `

    which shows as 65_function UBASE (find

    To calculate a divisio

    which transformed to

    NOTE: Recall thakeystroke combinati

    SG49A.book Page 11 Friday, September 16, 2005 1:31 PM unitslation examples using the ALG operating mode. Be ultiplying or dividing quantities with units, you must ty with its units between parentheses. Thus, to enter, product 12.5m 5.2 yd, type it to read


    (myd). To convert to units of the SI system, use it using the command catalog, N):

    n, say, 3250 mi / 50 h, enter it as (3250_mi)/(50_h) `

    SI units, with function UBASE, produces:

    t the ANS(1) variable is available through the on (associated with the ` key).

  • Addition and subtraction can be performed, in ALG mode, without using parentheses, e.g., 5 m + 3200 mm, can be entered simply as

    5_m + 3200_mm `.More complicated expression require the use of parentheses, e.g.,

    (12_mm)*(1_cm^2)/(2_s) `:Stack calculations in the RPN mode do not require you to enclose the different terms in pare

    3These operations prod

    Unit conversionThe UNITS menu cfollowing functions:

    Examples of function UNIT/TOOLS functionguide.For example, to conve

    CONVERT(x,y) convUBASE(x) convUVAL(x) extraUFACT(x,y) factoUNIT(x,y) comb

    SG49A.book Page 12 Friday, September 16, 2005 1:31 PMPage 3-12

    ntheses, e.g., 12 @@@m@@@ `1.5 @@yd@@ `*250 @@mi@@ `50 @@@h@@@ `/uce the following output:

    sontains a TOOLS sub-menu, which provides the

    CONVERT are shown below. Examples of the other s are available in Chapter 3 of the calculators users

    rt 33 watts to btus use either of the following entries:CONVERT(33_W,1_hp) `CONVERT(33_W,11_hp) `

    ert unit object x to units of object yert unit object x to SI unitsct the value from unit object xrs a unit y from unit object xines value of x with units of y

  • Page 3-13

    Physical constants in the calculatorThe calculators physical constants are contained in a constants libraryactivated with the command CONLIB. To launch this command you could simply type it in the stack: ~~conlib`, or, you can select the command CONLIB from the command catalog, as follows: First, launch the catalog by using: N~c. Next, use the up and down arrow keys to select CONLIB. Finally, press @@OK@@. Press `, if needed. Use the up the list of constants inThe soft menu keys include the following

    (*) Activated only if thThis is the way the tooption VALUE is selec

    To see the values of tthe @ENGL option:

    SI whenENGL when

    (*)UNIT whenVALUE whenSTK copieQUIT exit co

    SG49A.book Page 13 Friday, September 16, 2005 1:31 PMand down arrow keys () to navigate through your calculator.corresponding to this CONSTANTS LIBRARY screen functions:

    e VALUE option is selected.p of the CONSTANTS LIBRARY screen looks when the ted (units in the SI system):

    he constants in the English (or Imperial) system, press

    selected, constants values are shown in SI units (*) selected, constants values are shown in English units

    selected, constants are shown with units attached (*) selected, constants are shown without unitss value (with or without units) to the stacknstants library

  • If we de-select the UN(English units selected

    To copy the value of @STK, then, press @QUIlook like this:

    The display shows where, Vm, is the tagnumber will ignore th

    which produces:

    The same operation (after the value of Vm

    SG49A.book Page 14 Friday, September 16, 2005 1:31 PMPage 3-14

    ITS option (press @UNITS ) only the values are shown in this case):

    Vm to the stack, select the variable name, and press T@. For the calculator set to the ALG, the screen will

    hat is called a tagged value, Vm:359.0394. In of this result. Any arithmetic operation with this e tag. Try, for example:2*`

    in RPN mode will require the following keystrokes was extracted from the constants library):


  • Page 3-15

    Defining and using functionsUsers can define their own functions by using the DEFINE commandavailable thought the keystroke sequence (associated with the2 key). The function must be entered in the following format:

    Function_name(arguments) = expression_containing_arguments

    For example, we could define a simple function

    Suppose that you hadiscrete values and, tand get the result yoright-hand side for eassume you have setsequence of keystroke


    The screen will look li

    Press the J key, ansoft menu key (@@@H@@). The screen will show

    Thus, the variable H c

    This is a simple procalculator. This prog20 and 21 in the cal

    Ch03_RealNumbersQS.fm Page 15 Friday, February 24, 2006 6:19 PMH(x) = ln(x+1) + exp(-x)

    ve a need to evaluate this function for a number ofherefore, you want to be able to press a single buttonu want without having to type the expression in theach separate value. In the following example, we your calculator to ALG mode. Enter the followings:



    ke this:

    d you will notice that there is a new variable in your To see the contents of this variable press @@@H@@.now:

    ontains a program defined by:


    gram in the default programming language of theramming language is called UserRPL (See Chaptersculators users guide). The program shown above is

  • relatively simple and consists of two parts, contained between the programcontainers

    This is to be interpreted as saying: enter a value that is temporarilyassigned to the name x (referred to as a local variable), evaluate theexpression between qevaluated expression.

    To activate the functfollowed by the 2`. S

    In the RPN mode, topress the soft menu example, you could tbe entered by using:

    ReferenceAdditional informatiois contained in Chapt

    Input: x x

    Process: LN(x+1) + EXP(x)

    Ch03_RealNumbersQS.fm Page 16 Friday, February 24, 2006 6:19 PMPage 3-16

    uotes that contain that local variable, and show the

    ion in ALG mode, type the name of the functionargument between parentheses, e.g., @@@H@@@

    ome examples are shown below:

    activate the function enter the argument first, thenkey corresponding to the variable name @@@H@@@ . Forry: 2@@@H@@@ . The other examples shown above can1.2@@@H@@@ , 2`3/@@@H@@@.

    n on operations with real numbers with the calculatorer 3 of the users guide.

  • Page 4-1

    Chapter 4Calculations with complex numbersThis chapter shows examples of calculations and application of functions to complex numbers.

    DefinitionsA complex number znumbers, and i is thnumber x + iy has a rThe complex number the xy plane, with treferred to as the imaA complex number representation. An alA complex number c

    representation) as z =

    is the magnitude of ththe argument of the cThe relationship becomplex numbers is complex conjugate o= re i . The complez about the real (x) acan be thought of as

    Setting the caTo work with complex

    The COMPLEX mode option _Complex che

    SG49A.book Page 1 Friday, September 16, 2005 1:31 PM is a number z = x + iy, where x and y are real e imaginary unit defined by i = 1. The complex eal part, x = Re(z), and an imaginary part, y = Im(z). z = zx + iy is often used to represent a point P(x,y) in he x-axis referred to as the real axis, and the y-axis ginary axis. in the form x + iy is said to be in a rectangularternative representation is the ordered pair z = (x,y). an also be represented in polar coordinates (polar

    rei = rcos + i rsin, where r = |z| = e complex number z, and = Arg(z) = arctan(y/x) is omplex number z. tween the Cartesian and polar representation of given by the Euler formula: ei i = cos + i sin. The f a complex number (z = x + iy = re i) is = x iyx conjugate of i can be thought of as the reflection of xis. Similarly, the negative of z, z = x iy = re i, the reflection of z about the origin.

    lculator to COMPLEX mode numbers select the CAS complex mode:

    H )@@CAS@

    will be selected if the CAS MODES screen shows the cked, i.e.,

    22yx +


  • Press @@OK@@ , twice, to r

    Entering compleComplex numbers inCartesian representacalculator will be sexample, with the cal(3.5, -1.2), is entered


    A complex number cALG mode, 3.5-1.2i i


    In RPN mode, theskeystrokes:


    (Notice that the chanbeen entered, in the o

    NOTE: to enter thekey.

    SG49A.book Page 2 Friday, September 16, 2005 1:31 PMPage 4-2

    eturn to the stack.

    x numbers the calculator can be entered in either of the two tions, namely, x+iy, or (x,y). The results in the hown in the ordered-pair format, i.e., (x,y). For culator in ALG mode, the complex number as:


    an also be entered in the form x+iy. For example, in s entered as (accept mode changes):5 -1.2*`

    e numbers could be entered using the following


    ge-sign keystroke is entered after the number 1.2 has pposite order as the ALG mode exercise).

    unit imaginary number alone type , the I

  • Page 4-3

    Polar representation of a complex numberThe polar representation of the complex number 3.5-1.2i, entered above, is obtained by changing the coordinate system to cylindrical or polar (using function CYLIN). You can find this function in the catalog (N). You can also change the coordinate to polar using H. Changing to polar coordinate with standard notation and the angular measure in radians, produces the result in RPN mode:

    The result shown ab0.33029. The angReturn to Cartesian (available in the carepresentation is writinto the calculator bysymbol () can be enumber z = 5.2e1.5i,stack, before and afte

    Because the coordincalculator automaticcoordinates, i.e., x (0.3678, 5.18).On the other hand, if(use CYLIN), enteringnumbers, will produccoordinates, enter thstack, before and afte

    SG49A.book Page 3 Friday, September 16, 2005 1:31 PMove represents a magnitude, 3.7, and an angle le symbol () is shown in front of the angle measure.or rectangular coordinates by using function RECT talog, N). A complex number in polar

    ten as z = rei. You can enter this complex number using an ordered pair of the form (r, ). The angle ntered as ~6. For example, the complex can be entered as follows (the figures show the RPN r entering the number):

    ate system is set to rectangular (or Cartesian), the ally converts the number entered to Cartesian = r cos , y = r sin , resulting, for this case, in

    the coordinate system is set to cylindrical coordinates a complex number (x,y), where x and y are real

    e a polar representation. For example, in cylindrical e number (3.,2.). The figure below shows the RPN r entering this number:

  • Simple operations with complex numbersComplex numbers ca(+-*/). that i2= -1. Operatireal numbers. For exset to Complex, try th

    The CMPLX mThere are two CMcalculator. One is Chapter 3) and one dmenus are presented

    CMPLX menu thAssuming that systemthe CMPLX sub-men9@@OK@@ . T

    SG49A.book Page 4 Friday, September 16, 2005 1:31 PMPage 4-4

    n be combined using the four fundamental operations The results follow the rules of algebra with the caveat ons with complex numbers are similar to those with ample, with the calculator in ALG mode and the CAS e following operations:

    (3+5i) + (6-3i) = (9,2);(5-2i) - (3+4i) = (2,-6)(3-i)(2-4i) = (2,-14);

    (5-2i)/(3+4i) = (0.28,-1.04)1/(3+4i) = (0.12, -0.16) ;

    -(5-3i) = -5 + 3i

    enusPLX (CoMPLeX numbers) menus available in the available through the MTH menu (introduced in irectly into the keyboard (). The two CMPLX next.

    rough the MTH menu flag 117 is set to CHOOSE boxes (see Chapter 2), u within the MTH menu is accessed by using: he functions available are the following:

  • Page 4-5

    The first menu (options 1 through 6) shows the following functions:

    Examples of applications of these functions are shown next in RECT

    coordinates. Recall argument, while in RPthe function. Also, rlabels by changing th

    RE(z) Real part of a complex numberIM(z) Imaginary part of a complex numberCR(z) Separates a complex number into its real and imaginary

    partsRC(x,y) Form

    yABS(z) CalcARG(z) CalcSIGN(z) Calc

    |z|.NEG(z) ChanCONJ(z) Prod

    SG49A.book Page 5 Friday, September 16, 2005 1:31 PMthat, for ALG mode, the function must precede the N mode, you enter the argument first, and then select ecall that you can get these functions as soft menu e setting of system flag 117 (See Chapter 2).

    s the complex number (x,y) out of real numbers x and

    ulates the magnitude of a complex number.ulates the argument of a complex number.ulates a complex number of unit magnitude as z/

    ges the sign of zuces the complex conjugate of z

  • CMPLX menu in keyboardA second CMPLX menu is accessible by using the right-shift option associated with the 1 key, i.e., . With system flag 117 set to CHOOSE boxes, the keyboard CMPLX menu shows up as the following screens:

    The resulting menu inprevious section, namalso includes functioncombination

    Functions appMany of the keyboardChapter 3 for real ncomplex numbers. Tthe following example

    SG49A.book Page 6 Friday, September 16, 2005 1:31 PMPage 4-6

    clude some of the functions already introduced in the ely, ARG, ABS, CONJ, IM, NEG, RE, and SIGN. It i which serves the same purpose as the keystroke .

    lied to complex numbers-based functions and MTH menu functions defined in umbers (e.g., SQ, LN, ex, etc.), can be applied to he result is another complex number, as illustrated in s.

  • Page 4-7

    Function DROFunction DROITE takeand x2+iy2, and retuthat contains the pobetween points A(5, Algebraic mode):

    Function DROITE is calculator is in APPRO

    ReferenceAdditional informatioChapter 4 of the calc

    NOTE: When usincomplex numbers tangular measure scalculation of these

    SG49A.book Page 7 Friday, September 16, 2005 1:31 PMITE: equation of a straight lines as argument two complex numbers, say, x1 + iy1rns the equation of the straight line, say, y = a + bx, ints (x1, y1) and (x2, y2). For example, the line -3) and B(6, 2) can be found as follows (example in

    found in the command catalog (N). If the X mode, the result will be Y = 5.*(X-5.)-3.

    n on complex number operations is presented in ulators users guide.

    g trigonometric functions and their inverses with he arguments are no longer angles. Therefore, the elected for the calculator has no bearing in the functions with complex arguments.

  • SG49A.book Page 8 Friday, September 16, 2005 1:31 PM

  • Page 5-1

    Chapter 5Algebraic and arithmetic operationsAn algebraic object, or simply, algebraic, is any number, variable name or algebraic expression that can be operated upon, manipulated, and combined according to the rules of algebra. Examples of algebraic objects are the following:

    Entering algeAlgebraic objects caquotes directly into sFor example, to entelevel 1 use:

    An algebraic object cto the stack, or operaof the Equation Writethe following algebra

    After building the obmodes shown bel