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We need to find values of $z$ where it is multiplied by itself $n$ times and is equal to $re^{i\theta}.$ \\So, let $z=se^{i\theta}.$\\ Thus, we have $s^n=r.$\\ Hence, $s=\sqrt[n]{r}$\\  To solve for $\theta$, we have $n\theta= \theta +2\pi k$, for some $k\in\mathbb{Z}$ \\  Then $\theta=\frac{\theta + 2 \pi k}{n}$\\  Therefore we have $z=\sqrt[n]{r}e^i$ $z=\sqrt([n]{r}e^{i\frac{\theta +2 \pi k}{n}})$  \end{proof}  \end{problem}