FINAL EXAM (VERSION C)
Name:
This test has 8 pages and 7 problems.
No calculators are allowed. You are permitted only a pencil or pen. Work out everything as far as you can before making decimal approx-imations.
1. Find all solutions z to the equation tanhz = 1 .
Date: May 6, 2002.
3. Calculate the integral Z
C
cosz z(z2+ 8)dz
4. Calculate the integral Z
|z|=1
cos (1/z)dz z2sin (1/z).
5. Show that the map
w=
z−1
z+ 1 1/2
–1 –0.5
0.5 1
–1 –0.5 0.5 1 1.5 2
7. Suppose that f(z) is an entire analytic function, and that the real part off(z), which we will callu(x, y), has an upper bound:
u(x, y)≤u0