2.2 The Complex Plane Objective: to find the magnitude and argument of a complex number.

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2.2 The Complex Plane Objective: to find the magnitude and argument of a complex number

Graphing Complex Numbers To 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. i So the complex number 3+2i 3 + 2i would be in the R first quadrant.

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

Formula The formula to find the magnitude is Find the magnitude of: |-2 + 7i| |-4 – 3i|

Norm The 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)

Argument The 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)= ___ arg(-2 – 4i)

Practice Find the magnitude and argument (in degrees) of the following complex numbers i 2 + i Find the norm of the same numbers. How do they compare to the magnitude?

Notecard Make yourself a pocket mod with the formulas for the new vocabulary terms:pocket mod Conjugate Norm Magnitude Argument

Practice 1. 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 = i, find the magnitude and argument of iz. 7. Assignment: Worksheet