Complex Analysis
Spring 2001
Homework II Solutions
1. With defined to be the least positive zero of cos t, we established in class Wednesday 2 that t eit was onto the first quadrant of the unit circle
Complex Analysis
Spring 2001
Homework I Due Friday April 13
1. Conway, Chapter 1, section 3, problem 3. 2. The equation az + b + c = 0 can have solution set consisting of a single point, or a z line i
Complex Analysis
Spring 2001
Homework I Solution
1. Conway, Chapter 1, section 3, problem 3. Describe the set of points satisfying the equation |z - a| - |z + a| = 2c, where c > 0 and a R. To begin, w
Complex Analysis
Spring 2001
Homework II Due Friday April 20
1. With defined to be the least positive zero of cos t, we established in class Wednesday 2 that t eit was onto the first quadrant of the u
Complex Analysis
Spring 2001
Homework III Solutions
1. Conway, chapter 3, section 3, problem 8 If T z =
az + b show that T (R ) = R if cz + d and only if a, b, c, d can be chosen to be real numbers. I
Complex Analysis
Spring 2001
Homework IV Due Friday May 11
1. Conway, chapter 4, section 2, problem 10.
Before working on the next problem, be sure to review Prop. 1.6 in Chapter 3. 2. Conway, chapter
Complex Analysis
Spring 2001
Homework IV Solutions
1. Conway, chapter 4, section 2, problem 10. z2 + 1 Evaluate dz where (t) = reit for t [0, 2] for all possible values of r, z(z 2 + 4) 0 < r < 2 and
Complex Analysis
Spring 2001
Homework V Solutions
1. Conway, chapter 4, section 5, problem 7. Let (t) = 1 + eit for 0 t 2. Find ( z )n dz for all positive integers n. z-1
2i By Corollary 5.8, this is
Complex Analysis
Spring 2001
Homework VI Due Friday June 1
1. Conway, chapter 5, section 1, problem 1 b,h,i,j. 2. Conway, chapter 5, section 1, problem 4. 3. Conway, chapter 5, section 1, problem 13.
Complex Analysis
Spring 2001
Homework VI Due Friday June 1
1. Conway, chapter 5, section 1, problem 1 b,h,i,j. Determine the nature of the isolated singularity at z = 0 of the following functions. If