Convergent Complex Sequence/Examples/(1 over 2 + i 4 over 5)^n

Example of Convergent Complex Sequence
Let $\sequence {z_n}$ be the complex sequence defined as:
 * $z_n = \paren {\dfrac 1 2 + i \dfrac 4 5}^n$

Then:
 * $\displaystyle \lim_{n \mathop \to \infty} z_n = 0$

Proof
Thus $\cmod {z_n} \to 0$ and so $z_n \to 0$ as $n \to \infty$.