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Veva Garcia edited untitled.tex
almost 8 years ago
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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, starting with $z^n=w.$
\end{proof}
\end{problem}