Department of Mathematics
Christopher Newport University
Math 355-01 Complex Variables Spring Term 2009
Homework # 6
Due Friday March 6, 2009
1. Evaluate the integral in two different ways (a) directly, (b) by rewriting the integral as the sum of the integrals of the
real and imaginary part of the integrand.
Zπ/2
0
e(2 −i)tdt
2. Evaluate each integral
(a) Z1
0
dt
t+i(b) Zπ
0
sin(t+i)dt
3. Do problem # 7 on page 135.
4. Let f(z) = 2 z+ 1.Evaluate ZC
f(z)dz for the following contour C.
(a) z=ei θ,π
2≤θ≤3π
2
(b) Cis the closed contour C1+C2+C3where
C1:y=x2,from (0,0) to (1,1)
C2: the line segment from (1,1) to (2,0)
C3: part of the x-axis from (2,0) to (0,0)