Let u(x,y) = e" (xcos y-y siny) (a) Show that u(x,y) is a harmonic function. (b) If v(x,y) is a harmonic Conjugate of u, find v(x,y). (c) Use the answers in part (a) and (b) to find an analytic function f(z) that satisfies. Use Cauchy-Riemann theorem to show that f'(z) = e* (z+1) (d)

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