Patrick Corn
Math 185, summer 2005
Homework 9
Due 7/26/05
Problem 1: Let a1,...,anbe points on the unit circle. Show that there is some other point
pon the unit circle such that the product of the distances from pto ai, 1 ≤i≤n, is at least 1.
(Hint: Maximum Modulus Principle!)
Problems 2-7: VIII.4.1, VIII.7.2, VIII.7.5, VIII.12.1, VIII.12.2, VIII.12.3.
Problem 8: (Prelim exam, spring 1981) Suppose that fand gare entire functions such that
|f(z)| ≤ |g(z)|for all z∈C. Show that f(z) = cg(z) for some constant c. (Hint: Think about the
singularities of f/g.)
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