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So $w=re^{i\theta}$ for some non-negative $r\in\mathbb{R}$ and $\theta\in\mathbb{R}$ such that $-\pi\le\theta\le\pi$.\\  Then,  \begin{align*}  z^{n}&=re^{i\theta} z^{n}&=re^{i\theta}\\  &=re^{i\theta}e^{(2\pi m)i} m)i}\\  &=re^{i(\theta+2\pi m} m}\\  \end{align*}  \end{solution}  \end{document}