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\begin{align*}  z=\sqrt[n]{z^{n}}=\sqrt[n]{r}e^{\frac{i(\theta+2\pi m)}{n}}  \end{align*}  Note that $m\leq n$ because if If  $m>n$, then $m=n+k$ $m=qn+k$  for some $q\in\mathbb{Z}$ and some  positive integer $k$.\\ $0\leq k   Then,   \begin{align*}  e^{\frac{i(\theta+2\pi m)}{n}} &=e^{\frac{i\theta}{n}}e^{\frac{i2\pi (n+k)}{n}}\\