Department of Mathematics
Christopher Newport University
Math 355-01 Complex Variables Spring Term 2007
Homework # 7
Due Friday March 23, 2007
1. Evaluate each integral, where the the path is any contour between the indicated limits of integration:
(a) Zπ+i
i
sin(z
2)dz
(b) Zi
0
z ezdz
2. Do problem # 4 on page 133.
3. Let Cbe the lower half of the circle centered at the origin with radius 2 ,and with positive orientation. Evlauate
RC
1
zdz
Use the following branch of log z
log z= ln r+i θ (r > 0,π
2< θ < 5π
2)
4. Let Cbe the unit circle centered at the origin with positive orientation (counterclockwise). Evaluate each integral
(Hint: Use partial fractions.)
(a) ZC
1
z(z+ 2) dz
(b) ZC
1
z2(z+ 2) dz