Convergent Complex Sequence/Examples/(cos pi over n+1 + i sin pi over n+1)^n

Example of Convergent Complex Sequence
Let $\sequence {z_n}$ be the complex sequence defined as:
 * $z_n = \paren {\cos \dfrac \pi {n + 1} + i \sin \dfrac \pi {n + 1} }^n$

Then:
 * $\displaystyle \lim_{n \mathop \to \infty} z_n = -1$