Power of Complex Number minus 1/Corollary

Theorem
Let $z \in \C$ be a complex number.

Then:
 * $\displaystyle \sum_{k \mathop = 0}^{n - 1} z^k = \prod_{k \mathop = 1}^{n - 1} \paren {z - \alpha^k}$

where $\alpha$ is a primitive complex $n$th root of unity.