# Complex Variable question

• Dec 24th 2011, 07:45 AM
flaming
Complex Variable question
I am not sure if I am posting this in the correct section, please do let me know if I am in the wrong section.
I need help with the question below

Prove that $\overline{z}^k = \overline{z^k}$ for every integer k, where we assume that $z\not=0$ when $k$ is negative.
• Dec 24th 2011, 07:54 AM
emakarov
Re: Complex Variable question
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 $\overline{z_1z_2}=\overline{z}_1\cdot\overline{z}_ 2$.