Math 336 Midterm, April 27, 2011

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

1. Let Ω be an open connected set in ℂ. Suppose f and \overline{f} are analytic on Ω. Prove that f is constant. midterm 2

2. Suppose f is an entire function and |f(z) − 1| > 1 for all z. Prove that f is constant. midterm 3

3. Compute ∫_{|z−3|=2} \frac{e^{z}dz}{z(z − 2)}.

midterm 4

4. Compute ∫_{|z|=1} \frac{|dz|}{|z − 2|^{2}} .