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\title{Math 336 Midterm, April 26, 2010}
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Name:\hrulefill

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One notebook sized page of notes is allowed on the test. 

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\item Let $\ds \Omega$ be an open connected set in $\mathbb{C}$. Suppose $f$ 
and $\ds \overline{f}$ are analytic on $\ds \Omega$.  Prove that $f$ is
constant.

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\item Suppose $f$ is an entire function and $\ds |f(z)-1|>1$ for all $z$. 
Prove that $f$ is constant.

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\item Compute 
\[
\int_{|z-3|=2}\frac {e^zdz}{z(z-2)} .
\]

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\item Compute 
\[
\int_{|z|=1} \frac{|dz|}{|z-2|^2}.
\]

\end{enumerate}

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