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Magnitude The distance between (0, 0) and x + yi is its MAGNITUDE, denoted by |z|. In other words, it is the length of the hypotenuse of the triangle formed by graphing the point. To find the magnitude of the complex number 3 + 2i, draw the triangle and find the length of its hypotenuse. 2 |z| = 3
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2.2 The Complex Plane Objective: to find the magnitude and
argument of a complex number
Graphing Complex NumbersTo graph a complex number on a plane, we
have to change the x-axis to represent the real part of the number and change the y-axis to represent the imaginary part.
iSo the complex number 3+2i
3 + 2i would be in the R
first quadrant.
MagnitudeThe distance between (0, 0) and x + yi is its MAGNITUDE , denoted by |z|. In other words, it is the length of the hypotenuse of the triangle formed by graphing the point.
To find the magnitude of the complex number 3 + 2i, draw the triangle and find the length of its hypotenuse.
2|z| =
31323 22
FormulaThe formula to find the magnitude is
Find the magnitude of:|-2 + 7i|
|-4 – 3i|
22|| yxz
NormThe norm of a complex number is denoted by
N(z) and is the product of the complex number and its conjugate.
N(z) =
Find N(-2 + 7i)
Find N(-4 – 3i)
zz
ArgumentThe argument of a complex number z, written
arg(z), is the measure of the angle in standard form with z on the terminal side.
To find the argument, you have to use trig.arctan(-4/-2)= ___ + 1800
arg(-2 – 4i)
PracticeFind the magnitude and argument (in degrees)
of the following complex numbers.
4 + 3i
2 + i
Find the norm of the same numbers. How do they compare to the magnitude?
NotecardMake yourself a pocket mod with the
formulas for the new vocabulary terms:
Conjugate
Norm
Magnitude
Argument
Practice1. Plot the point 4 + i.2. Find the exact magnitude.3. Find the norm.4. Find the argument.
5. Repeat with the point 3 – 2i.
6. If z = -2 + 2i , find the magnitude and argument of iz.
7. Assignment: Worksheet
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