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Let $0 < |\alpha| < 1$. Find $\displaystyle{\int_{\gamma}\frac{\mathrm{Re}(z)}{z-\alpha}dz}$

in terms of $\alpha$, where $\gamma$ is the circle $|z| = 1$ oriented in the counterclockwise direction.

I tried to express $\mathrm{Re}(z)$ as $\frac{z+\overline{z}}{2}$. Then how should I proceed on? Any idea/suggestion is welcomed!:D

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up vote 1 down vote accepted

Hint: Note that when $|z|=1$, $\bar{z}=\frac{1}{z}$.

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Ok! I got it! thanks! –  Alan Nov 18 '12 at 4:18
    
@Alan: You are welcome! –  23rd Nov 18 '12 at 7:26
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