this is for holding javascript data
Veva Garcia edited untitled.tex
almost 8 years ago
Commit id: bb9f97dd607511e67b38f1bc08ff44a5203bf779
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(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 $z^n=re^{i\theta}.$\\
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 $re^{i\theta}.$
\end{proof}
\end{problem}