Divergent Complex Sequence/Examples/(2 over 3 + 3i over 4)^n

Example of Divergent Complex Sequence
Let $\sequence {z_n}$ be the complex sequence defined as:
 * $z_n = \paren {\dfrac 2 3 + \dfrac {3 i} 4}^n$

Then $\ds \lim_{n \mathop \to \infty} z_n$ does not exist.

Proof
Thus $\cmod {z_n} \to \infty$ and so the limit does not exist.