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Let $n \in \mathbb{Z}$ and $w \in \mathbb{C}.$ So, in polar coordinates, $w=re^{i\theta}$ for some $r,\theta \in \mathbb{R}.$ Notice that the $r$ represents the modulus of the complex number and $\theta$ is the argument. So, we have $z^n=re^{i\theta}.$\\  Geometrically, we are multiplying the lengths and add their angles. \\  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 $n\theta= \theta +2\pik$, for some $k\in\mathbb{Z}$  \end{proof}  \end{problem}