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Question: use the cauchy riemann equations to prove that the function...

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Use the Cauchy Riemann equations to prove that the function f(:)- 3e analytic. Find the derivative of f( and express it as a function of z x iy only 5. (a) +iz is (7 marks) Givenu(x,y)-2(x2-Уг)-e-y cos(3x), find the conjugate function v(x,y)such that f()-x, y)+ iv(x. y) is an analytic function of z throughout the z plane Express fz) as a function of z only. (b) (7 marks) (c) Use the residue theorem to evaluate (2+4X-3) where C is the contour given by () 2, (i) -, (ii (11 marks)

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