Operations of Complex Numbers

|a+bi|

sqrt(a^2+b^2)

r in complex numbers name

modulus

theta in complex numbers name

argument

how to find theta in complex numbers

arctan(b/a)

Two Polar Forms of Complex Numbers

1. rcis(theta) 2. re^i(theta)

Multiplying Complex Numbers in polar form

Multiply moduli, add arguments

Dividing Complex Numbers in polar form

Divide moduli, subtract arguments

How to plot complex numbers in polar form?

Line 1: estimate line for unit circle point from theta
Line 2: Draw circle with radius r

Raising Complex Numbers to the nth power

Z^n = r^n cis(theta*n)

Finding nth Roots of Complex Numbers

Z^1/n = r^1/n cis(theta/n+2pik/n), k=0,...,n-1

Area of a polygon formed by its roots

n(1/2)(r)^1/n(r)^1/n(sin(2pi/n))