Complex Analysis     MATH 305

Homework Assignment #6

Due Thursday, April 7, START of Class

Homework should be turned in at the BEGINNING OF CLASS. All problem numbers refer to the primary course text by Brown and Churchill. Unless otherwise indicated, all parts of a problem (a), (b), etc. should be completed. You are encouraged to work on these problems with other classmates, although the solutions you turn in should be YOUR OWN WORK.

Important: Please list the names of any students or faculty who you worked with on the assignment. Also cite any references (website, other texts, etc.) that you may have used while working on this assignment.

Section 33 (p. 104): #1, 2

Sections 37 - 38 (p. 121): #2, 4
Note: For #2c you will need to do an improper integral and then explain why Re(z) > 0 is required. The point of #4 is to avoid having to use integration by parts (twice each time) to evaluate the two integrals on the right. In other words, using complex variables often makes real-variable integration much easier!

Section 39 (pp. 125 - 126): #5

Sections 40 - 42 (pp. 135 - 136): #1, 3

Section 43 (pp. 140 - 142): #1, 3
Hint: For #1 you will need to use the inequality |z1 - z2| ≥ | |z1| - |z2| |