MAT 709: Complex Function Theory - I
Fall 2007, 3 credits: Test 1
Dr. Pushkin Kachroo
http://www.ece.vt.edu/pushkin
pushkin@vt.edu
PROBLEM 1 : (10 points) For which nis ian nth root of unity?
PROBLEM 2 : (10 points) Sketch the image under the spherical projection of a line of
longitude X=√1−Z2cos θ,Y=√1−Z2sin θ, for θfixed and −1≤Z≤1.
PROBLEM 3 : (10 points) Consider the transformation ln z. Show the transformations
of (a)circles centered at the origin, (b)rays emanating from the origin, and (c)z-plane.
PROBLEM 4 : (10 points) Let u(x, y) = αand v(x, y) = β, where uand vare the real
and imaginary parts of an analytic function f(z) and αand βare any constants, represent
two families of curves. Prove that the families are orhogonal.