Convergent Complex Sequence/Examples/(cos pi over n + i sin pi over n)^2n+1

Example of Convergent Complex Sequence
Let $\sequence {z_n}$ be the complex sequence defined as:
 * $z_n = \paren {\cos \dfrac \pi n + i \sin \dfrac \pi n}^{2 n + 1}$

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