Construct the corresponding analytic function

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Question 1 - Show that the function x2 - y2 + 2y which is harmonic remains harmonic under the transformation z = w3.

Question 2 - Let f(z) = u(x, y) + iv(x, y) be an analytic function. If u = 3x - 2xy, then find v and express f(z) in terms of z.

Question 3 - Show that the function u(x, y) = 4xy - 3x + 2 is harmonic. Construct the corresponding analytic function

f(z) = u(x, y) + iv(x, y)

Express f(z) in terms of complex variable z.

Reference no: EM132580429

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