Power of Golden Mean as Sum of Smaller Powers

Theorem
Let $\phi$ denote the golden mean.

Then:
 * $\forall z \in \C: \phi^z = \phi^{z - 1} + \phi^{z - 2}$

Proof
Let $z \in \C$.

Let $w \in \C$ such that $w + 2 = z$.

Then: