Department of Mathematics
Christopher Newport University
Math 355-01 Complex Variables Spring Term 2007
Homework # 3
Due Friday Feb.2.07
1. Sketch the following sets and determine which are (i) connected, (ii) domain.
(a) Re z≥2
(b) −π
4< arg z < π
4
(c) {z:|z|<2 or |z−3i| ≤ 1}
2. Write the function f(z) = z+1
z,in the form f(z) = u(x, y) + i v (x, y).
3. Suppose that f(z) = x2−y2+ 2 x+i(2y−2xy).Write f(z) in terms of z, and simplify.
4. Find a region in the zplane whose image under the transformation w=z2is the square region in the wplane
bounded by the lines u=−1, u =−2, v = 1 ,and v= 3.
5. Find the image of the semi-infinite strip x≥1,−π
4< y ≤π
4under the transformation w= exp(z).