Department of Mathematics
Christopher Newport University
Math 355-01 Complex Variables Spring Term 2007
Homework # 1
Due Friday Jan.19.07
1. Do problems 8, 9 on page 5 and problem 5 on page 7.
2. Solve the equation z2+ 2 z+ 2 = 0 by writing
(x, y) (x, y) + 2 (x, y ) + (2,0) = (0,0)
and then solving a pair of simultaneous equations in xand y.
3. Reduce the quatity to a real number 4i
(1 + i) (2 + i) (3 + i)
4. Locate the numbers z1+z2and z1−z2vectorially when
(a) z1= (−2,1), z2= (1,1)
(b) z1= 3 i , z2= 3/2−2i
5.Sketch the set of points determined by the given conditions.
|z−2 + i| ≤ 2