Complex Numbers

De Moivre's Theorem

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


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