380_q_6 - be a contour in D starting at i and ending at...

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Math 380 Quiz 6 (Take-home) Due in class May 17, 2010 Name 1. (2 pts each) Let D = f x + iy : x > 0 and y > 0 g and f ( z ) = z 3 : (a) Sketch D: (b) Describe D using polar representations: D = re : _________ ± (c) Find the image of D under the function f: 2. (2 pts) Let D denote the complex plane with the ray ( ; 0] removed and let
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Unformatted text preview: be a contour in D starting at i and ending at & i: Find Z 1 z dz: 3. (2 pts) Suppose f and g are entire functions and j f ( z ) j < j g ( z ) j for all complex z: Use Liouville&s to prove that f ( z ) = cg ( z ) for some constant c: 1...
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