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Quiz6.EGM4313.solution

# Quiz6.EGM4313.solution - z = 29 1 1 2 2 i i-= Residue at 2...

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EGM 4313 NAME:_____________________________ Spring 2011 Quiz 6 Open book/Closed notes/No calculators or computers 25 minute time limit Evaluate the integral ( 29 ( 29 2 0 sin 5 4sin d π θ θ θ - . Solution: ( 29 ( 29 ( 29 ( 29 2 2 2 0 1 1 2 2 2 1 1 1 1 sin 1 1 2 2 1 5 4sin 2 5 2 2 5 1 1 1 1 5 4 4 1 2 2 2 z z z z z dz z i z d dz iz i z iz z z i z z z dz dz i i i i z z z z z i z π θ θ θ = = = = - - = = - - + - - - - = - = - - - - - Ñ Ñ Ñ Ñ Simple poles at 0 z = and 2 i z = inside the unit circle.
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Unformatted text preview: z = : ( 29 1 1 2 2 i i-= -- Residue at 2 i z = : 2 5 1 5 2 4 3 3 2 4 2 2 i i i i -- = = - - ( 29 ( 29 2 sin 1 5 2 1 5 4sin 4 3 3 d i i =--= - ∫...
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