Let z = x + iy ∈ C, and suppose u : C → R is given by u(z) = u(x, y) = 3(x^2)y  - y^3. (i) Verify that u satisfies Laplace’s equation, namely uxx + uyy = 0, for all z ∈ C. (ii) Find an analytic function f : C → C such that Re(f) = u. (Write your answer  as a function f(z) of the complex variable z = x + iy.)

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