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Fix a positive integer n and a complex number w. Find all solutions to $z^n=w.$\\  (Hint:write w in terms of polar coordinates.)  \begin{proof}  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 $z^n=re^{i\theta}$ $z^n=re^{i\theta}.$\\  Geometrically, we are multiplying the lengths and add their angles.  \end{proof}  \end{problem}