De Moivre's Formula/Integer Index

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

Then:
 * $\forall n \in \Z: \paren {r \paren {\cos x + i \sin x} }^n = r^n \paren {\map \cos {n x} + i \, \map \sin {n x} }$

Also known as
De Moivre's Theorem.