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Let $p(z)$ be a polynomial and $C$ denote the circle $|z-a| = R$. I want to evaluate the integral over $C$ of $p(z)$ with respect to $\overline{z}$, the conjugate of $z$.

I think to start off, I should probably use a Taylor expansions centered at $a$, but I'm lost with what to do next.

Any hints on how to approach this problem?

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up vote 1 down vote accepted

Imagine the circle shifted to the origin and scaled to the unit circle -- can you now express $\overline{z}$ in terms of $z$?

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