Complex Arithmetic/Examples

Example: $\paren {\dfrac {1 + \sqrt 3 i} {1 - \sqrt 3 i} }^{10}$
Let $z_1 = 2 + i$, $z_2 = 3 - 2 i$ and $z^3 = -\dfrac 1 2 + \dfrac {\sqrt 3} 2 i$.