# hw5_1 - Suggestion: Apply the Cauchy-Riemann equations to...

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Complex Variables Assignment 5.1 Spring 2011 Due October 3 Exercise 1. Let A be a connected open set and suppose that f and g are both analytic functions on A . Prove that if Re f = Re g everywhere on A then there is a purely imaginary number ik so that f = g + ik . In other words, the real part of an analytic function (almost) determines it completely. [
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Unformatted text preview: Suggestion: Apply the Cauchy-Riemann equations to the analytic function f-g .] Exercise 2. 1.5.16. Note that this exercise proves that if the image of an analytic function is contained in any xed line, then that function is actually constant. Exercise 3. 1.5.28 Exercise 4. 1.5.29...
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## This note was uploaded on 02/29/2012 for the course MATH 4364 taught by Professor Ryandaileda during the Fall '11 term at Trinity University.

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