Malorie's blog

11.2 Complex numbers

in order to do this lesson, you must know these formulas:
Rectangular - z=x + yi
Polar - z=rcos(theta) + rsin(theta)i
Abr: z=rcis(theta)

When multiplying complex numbers you must FOIL rectangular and multiply r's and add (theta)'s for polar.

Example 1:

Express 2cis150 in rectangular form
2cos50 + 2 sin50i - use formula
x=2cos50 y=2sin50 - use formula's
x=1.2286 y=1.532 - simplify
1.286 + 1.532i


Example 2:

3-4i
(square root of 3^2 + (-4)^2) = 5
(theta)= tan inverse of (-4/3) = 53.130
(find where tan is negative on the unit circle and then use the formula)
z= 5cis126.87 ; z= 5cis306.87