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SOLUTIONS TO HOMEWORK ASSIGNMENT # 7

SOLUTIONS TO HOMEWORK ASSIGNMENT # 7 1. Determine the nature of all singularities of the following functions f(z). (a) f(z) = cos1/z. (b) f(z) = 1 z2 sinz. (c) f(z) = z ez2 −1. Solution: (a) z = 0 is the only singularity. It is an essential singularity since the Laurent series expansion about z = 0, cos1/z = 11 2!z2 + 1 4!z4 +···,

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