# Complex Numbers

## Complex Roots

For a complex number

The roots can be found using the formula

## Finding Trig Identities

Trig identities can be found by equating complex numbers and using de moivre's theorem. The examples below are shown for n=2 but the process is the same for any n.

### Identities for

Using de moivre's theorem to equate

Expanding

Equating real and imaginary parts

### Identities for

To find the identity for , start with , and raise to the power of 2

Substituting in for the pairs of