De Moivre's Formula/Proof 1

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

Then:
 * $\forall \omega \in \C: \left({r \left({\cos x + i \sin x}\right)}\right)^\omega = r^\omega \cos \left({\omega x}\right)+ i \sin \left({\omega x}\right)$