Question: complex analysis about analytic functions Given the function u(x, y) = (x - 1)3 - 3xy? + 3y?. a) Find the domain of the function.

complex analysis about analytic functions

Given the function u(x, y) = (x - 1)3 - 3xy? + 3y?. a) Find the domain of the function. b) Show that u(x, y) is harmonic in its domain. c) Determine the corresponding analytic function f(=) = u(x,y) + iv(x,y) by finding the harmonic conjugate of u(x, y). d) Express the function f(=) in item (c) in terms of s, and then find its derivative f'(=)

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