MINDJOG 9/8MINDJOG 9/8

Foil:Foil:

1) (3+2x)(2x+3)1) (3+2x)(2x+3)

2) (3 – 2x)2) (3 – 2x)22

MINDJOG 9/9MINDJOG 9/9Simplify:Simplify:1)1)√√-72/180-72/180

2)2)Find f and g so Find f and g so that (2f + 3g) + that (2f + 3g) + (5f – 2g)i = 13 + (5f – 2g)i = 13 + 4i4i

OBJECTIVEOBJECTIVE

Students will learn Students will learn to add, subtract, to add, subtract, multiply and divide multiply and divide complex numberscomplex numbers

TERMSTERMSImaginary unit: Imaginary unit: negative number negative number inside a radicalinside a radical

Complex Number: a + Complex Number: a + bi, a is the real part, b bi, a is the real part, b is the imaginary partis the imaginary part

NOTESNOTES

i = √-1i = √-1ii2 2 = -1= -1ii3 3 = -i= -iii4 4 = 1= 1

ADDITION/SUBTRACTIONADDITION/SUBTRACTION

Add real #’s, add Add real #’s, add imaginary #’simaginary #’s

1)1)(3+4i)+(6-7i)(3+4i)+(6-7i)

2)2)(3+4i)-(6-7i)(3+4i)-(6-7i)

MULTIPLICATIONMULTIPLICATION

FOILFOIL

1)1)(3+4i)(6-7i)(3+4i)(6-7i)

2)2)(3+4i)(3+4i)22

DIVISIONDIVISION

No i’s in denominatorNo i’s in denominator Multiply by conjugateMultiply by conjugate

1)1)(3+4i)(3+4i)

(6-7i)(6-7i)

Simplify:Simplify:1)1) (6 + 5i) + (-3 – 7i)(6 + 5i) + (-3 – 7i)

2)2) (6 + 5i) - (-3 – 7i)(6 + 5i) - (-3 – 7i)

3)3) (6 + 5i)(-3 – 7i)(6 + 5i)(-3 – 7i)

4)4) (6 + 5i)/(-3 – 7i)(6 + 5i)/(-3 – 7i)

CLASSWORKCLASSWORK

Complex #’s DittoComplex #’s Ditto

HOMEWORKHOMEWORK

Finish DittoFinish Ditto

CLASSWORK (9/9)CLASSWORK (9/9)

Game Time (2Game Time (2ndnd sheet of Comp sheet of Comp #’s Packet)#’s Packet)

SIMPLIFYSIMPLIFY

(12 – 11i) + (4 – 9i)(12 – 11i) + (4 – 9i)

SIMPLIFYSIMPLIFY

(4 + 11i)(-3 – i)(4 + 11i)(-3 – i)

SIMPLIFYSIMPLIFY

(12 +6i) – (6 + 3i)(12 +6i) – (6 + 3i)

SIMPLIFYSIMPLIFY

(8 – 3i)(8 – 3i)22

SIMPLIFYSIMPLIFY

3(4 + 5i) – 2(1 – i)3(4 + 5i) – 2(1 – i)

SIMPLIFYSIMPLIFY

)1421(7

3)189(

9

2ii

SIMPLIFYSIMPLIFY

-3i(3 – 2i)-3i(3 – 2i)

SIMPLIFYSIMPLIFY

(16 + 23i) + (-16 + (16 + 23i) + (-16 + 29i) – (25 – i)29i) – (25 – i)

SIMPLIFYSIMPLIFY

)9

2

3

4()

9

7

3

2( ii

SIMPLIFYSIMPLIFY

i22

5

SIMPLIFYSIMPLIFY

(5 + 2i)(5 + 2i)33

SIMPLIFYSIMPLIFY

Find p and qFind p and q so so that (5p – q) + that (5p – q) + (2q + 4p)i = 36 + (2q + 4p)i = 36 + 26i26i

SIMPLIFYSIMPLIFY

i117

2

HOMEWORK (9/9)HOMEWORK (9/9)

p. 109 #’s 38 – p. 109 #’s 38 – 68, 84 – 94, even68, 84 – 94, even