Complex Variable question

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I need help with the question below

Prove that $\displaystyle \overline{z}^k = \overline{z^k}$ for every integer k, where we assume that $\displaystyle z\not=0$ when $\displaystyle k$ is negative.

Re: Complex Variable question

This follows from the fact that $\displaystyle \overline{1/z}=1/\overline{z}$ and $\displaystyle \overline{z}^k = \overline{z^k}$ for positive $\displaystyle k$. The latter fact follows by induction from $\displaystyle \overline{z_1z_2}=\overline{z}_1\cdot\overline{z}_ 2$.