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Let u(x, y) = x^3 + kxy^2 + y. (a) Determine the value of k such...

Let u(x, y) = x^3 + kxy^2 + y. (a) Determine the value of k such that u is an harmonic function. (b) Find the harmonic conjugate v of u. (c) Obtain the expression of f = u + iv in terms of z = x + iy

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