hw10_1 - f is analytic if and only if f has an...

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Complex Variables Assignment 10.1 Spring 2011 Due November 7 Exercise 1. Suppose that f is entire and lim z →∞ f ( z ) z = 0. Prove that f is constant. Exercise 2. Show that if f is entire and lim z →∞ f ( z ) = then f is surjective. Exercise 3. Let A C be a simply connected open set and f : A C a continuous function. Show that
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Unformatted text preview: f is analytic if and only if f has an antiderivative. Exercise 4. Let A C be a connected open set and let f be an analytic function on A . Prove that if f is nonconstant and nonzero on A then | f | cannot attain a global minimum on A ....
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