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\end{problem}  \begin{solution}  Let $n\in\mathbb{Z}$ and $w\in\mathbb{C}$.\\  So $w=re^{i\theta}$ for some non-negative $r\in\mathbb{R}$ and $\theta\in\mathbb{R}$ such that $-\pi\le\theta\le\pi$.\\ $\theta\in\mathbb{R}$.\\  Then,  \begin{align*}  z^{n}&=re^{i\theta}\\