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