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Math3364-PracticeFinal-F10

Math3364-PracticeFinal-F10 - Last Name First Name Signature...

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Last Name: First Name: Signature: Student I.D. No.: Math 3364 Practice Final December, 2010 Two hours and twenty minutes University of Houston Instructions: 1. Put your name, signature and I.D. No. in the blanks above. 2. Answer the questions in the spaces provided, using the backs of pages or the blank page at the end for overflow or rough work. 3. Your grade will be influenced by how clearly you present your solutions. Justify your solutions carefully by referring to definitions and results from class where appropriate. 4. No calculators or cell phones permitted. Question Value Points 1 15 2 10 3 15 4 10 5 10 6 10 7 15 8 15 9 15 10 15 Total 120
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( 15 points) 1. (a) Find the argument of the following number and write it in polar form: arg[(1 i )( 3 + i )] = (b) True or false: Every power series at z 0 with radius of convergence R > 0 converges uniformly to an analytic function f ( z ) on the open disk { z C : | z z 0 | < R } . circle: TRUE or FALSE. (c) The residue of ze z/ 3 at z = 0 is: 2
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( 10 points) 2. What equation(s) do x and y have to satisfy if z = x + iy satisfies z 2 + z 2 = 2?
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