De Moivre's Formula

Theorem
Let $z \in \C$ be a complex number expressed in complex form:
 * $z = r \left({\cos x + i \sin x}\right)$

Then:
 * $\forall n \in \Z_{> 0}: \left({r \left({\cos x + i \sin x}\right)}\right)^n = r^n \cos \left({n x}\right)+ i \sin \left({n x}\right)$

Exponential Form
De Moivre's Formula can also be expressed thus in exponential form:

Also known as
De Moivre's Theorem.