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I.1.1
Identify and sketch the set of
(a) jz 1 ij = 1
(f)
(b) 1 < j2z 6j < 2
(g)
(c) jz 1j2
Mathematics 27000
Problem Set #1
Due April 10, 2014
From Gamelin: I.1
I.2
I.4
I.8
#5
#2
#1
#1,5,8
1. Working directly from the denition of complex dierentiability, nd the values of z C such that the function f (z) = |z|2 is not complex dierentiable.
2. Fi
Mathematics 27000
Midterm Exam
May 6, 2014
Solve all the problems, showing all your work clearly.
1. Let D = cfw_z C | 0 < |z 1| < 1. Does every harmonic function on D have
a harmonic conjugate? Either prove the answer is yes, or give a counterexample.
An