MTH 611 Complex Analysis
Homework Assignment II
Solutions
Problem I.
(i) Expand f (z ) = (2z + 1)/(z + 1)2 as power series f (z ) = n=0 an (z 1)n . What is
the radius of convergence of the resulting s
MTH 611 Complex Analysis
Homework Assignment I
Due April 16, 2012
Problem I.
2i
.
(1 + 2i)(2 + i)
(ii) Find the real and imaginary parts of (1 i 3)19 .
(iii) Solve completely z 5 = 4 3i.
(i) Simplify
MTH 611 Complex Analysis
Homework Assignment IV
Solutions
Problem I.
(i) Let f (z ) be entire and suppose that f (z ) is real if and only if z is real. Show that
f (z ) can have at most one zero.
Solu
MTH 611 Complex Analysis
Midterm Exam Solutions
Problem I.
(i) Is the function f (z ) = f (x + iy ) = sin x cosh y i cos x sinh y analytic?
Solution. We compute
u
v
= cos x cosh y =
= cos x cosh y,
x
MTH 611 Complex Analysis
Exam Sample Problems
Problem I.
(i) Find all analytic functions f on an open, connected C such that |f |2 is harmonic
in .
1+x
y
(ii) Is f (z ) =
+i
analytic?
2 + y2
(1 + x)
(
MTH 611 Complex Analysis
Homework Assignment III
Solutions
Problem I.
(i) Find precise conditions under which the principal branch of the complex Log function satises the familiar identity Log (zw) =