Complex Analysis I
Exam 1
1. Prove that if z and w are complex numbers with |z | = 1, then
zw
= 1.
1 zw
2. Prove that if f (z ) is analytic, then f (z ) is analytic.
3. Let f (z ) = |z |2 = x2 + y 2 .
a. Show that f (z ) exists at z = 0.
b. Show that f (z
Complex Analysis
Here are some sample problems from the text by Brown and Churchill. These are less abstract and
more basic than most of the problems in Greene and Krantz text, but I still think theyd be good practice
problems for the rst exam in this cla
Complex Analysis
Some more sample problems from the text by Brown and Churchill. As on the last sheet of sample
problems I handed out, these problems are more straightforward than most of the ones in Greene and Krantz
text. Some should be quite easy, some
Math 5423
Review for Exam 1
The rst exam will cover chapters 1 and 2 of the text. In the lectures we have followed the sequence of
topics in the text pretty closely, which means that an easy way to review for the test is just to re-read these
two chapters
Solutions to problems on Assignment 7
9. We will prove the converse of the desired statement. That is, we assume there exists N Z such that
for every sequence zn in D(P, r)\cfw_P with lim zn = P , there exists n N such that |(zn P )N f (zn )| N ;
and we
Complex Analysis I
Exam 2
1. Dene f : (0, ) R by f (x) = sin(log x).
a. Find the values of x (0, ) at which f (x) = 0.
b. Use the result of part a to answer the question: can f be extended to an entire
function on the complex plane?
2. Suppose f = u + iv
Math 5423
What Exam 2 Covers
The second exam will cover all of chapter 3 and sections 4.1 through 4.5 of the text.
As was true for the rst two chapters, there were only minor dierences between the presentation in
the book and the lectures, apart from the