Fall 2011-MTH5130-Theory of a Complex Variable-Homework 5
1. Given n > 1, nd out how many non-zero complex numbers z exists such that one of the
nth degree roots of z is z . Plot all these complex num
Fall 2011-MTH5130-Theory of a Complex Variable-Homework 6
1. Evaluate the integral
|z |zdz,
C
where C is the closed contour consisting of the upper semicircle |z | = 1 and the
segment 1 x 1, y = 0.
2.
Fall 2011-MTH5130-Theory of a Complex Variable-Homework 4
1. A function u(x, y ) which in some domain possesses continuous partial derivatives up to
second order inclusive and satises Laplaces equatio
Fall 2011-MTH5130-Theory of a Complex Variable-Homework 1
1. Perform the operations indicated:
2
; (1 + i 3)3 ;
1 3i
2. Find the modulus and argument (a and b are real numbers):
1 i; 2 5i; a + bi(a =
Fall 2011-MTH5130-Theory of a Complex Variable-Test 2
1. Evaluate the integral (without use of residues)
+
dx
.
+1
x4
0
2. Expand the function
z
z 2 2z + 5
in a Taylor series at the point z = 1 and nd