Question:Determine the nature of the singularitiesof each of the following functionsand evaluate the residues (a > 0):(e)zetiz2² + a²etiz22-a²(f)zetiz+ a².-k(h)2+1Hint. For the point at infinity, use the transformation w = 1/2 for|2| → 0. For the residue, transform f(z) dz into g(w) dw and look atthe behavior of g (w).0

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Answered: Determine the nature of the…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter8: Polynomials

Section8.5: Solution Of Cubic And Quartic Equations By Formulas (optional)

Problem 29E

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Determine the nature of the singularities of each of the following functions and evaluate the residues (a > 0): ze+iz 2² + a² etiz (h) zetiz 2²+ a² 0