Math3364-PracticeFinal-F10

Circle true or false c the residue of zez3 at z 0 is

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Unformatted text preview: C : |z − z0 | < R}. circle: TRUE or FALSE. (c) The residue of zez/3 at z = 0 is: 2 (10 points) 2. What equation(s) do x and y have to satisfy if z = x + iy satisfies z 2 + z 2 = 2? 3 (15 points) 3. Take u(x, y ) = xy − x + y + x2 − ky 2 , where the constant k is a real number. (a) If u is harmonic in the entire plane, what condition holds for the constant k ? (b) Assuming the constant k has been chosen so that u is harmonic, what is its harmonic conjugate v (up to a constant)? 4 (c) Assuming the constant k has been chosen so that u is harmonic, find the function f (z ) such that f (x + iy ) = u(x, y ) + iv (x, y ) and express it in terms of z . 5 2 (10 points) 4...
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This note was uploaded on 01/21/2014 for the course MATH 3364 taught by Professor Staff during the Fall '08 term at University of Houston.

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