# Complex Variable question

Prove that $\overline{z}^k = \overline{z^k}$ for every integer k, where we assume that $z\not=0$ when $k$ is negative.
This follows from the fact that $\overline{1/z}=1/\overline{z}$ and $\overline{z}^k = \overline{z^k}$ for positive $k$. The latter fact follows by induction from $\overline{z_1z_2}=\overline{z}_1\cdot\overline{z}_ 2$.