11-2

Things you should know:

• z = x + yi
• z = rcostheta + rsintheta i 
• z = rcistheta
• |z |= square root of x^2 + y^2
• To multiply complex numbers:

1. Foil for rectangular problems.
2. Multiply r and add theta for polar problems.

Example: 0 + i

What form is it in? Rectangular form.

Find r and theta.

r = square root of 0^2 + 0^2. 

r = 0 + 0 =0

theta = tan^-1(0)

 Theta = 0

When you put that on the quadrants, you will get 180 and 360.

So once you do that, your answers will be square root of 2 cis 180 degrees and -square root of 2 cis 360 degrees.

Example 2: 10 cis 20 degrees

• What form is it in? Polar form.
• Solve for x and y.
• x = 10cos20= 9.367
• y=10sin20= 3.420
• Final answer: 9.367 + 3.420

-Amber :P