Question: 4. (a) (3 points) Consider the function u(m, y) = $3333y2+1 and show that u is harmonic. (b) (6 points) Find a function f :

4. (a) (3 points) Consider the function u(m, y) = $3333y2+1 and show that u is harmonic. (b) (6 points) Find a function f : C > (C that is complex differentiable such that u is the real part of f. (c) (3 points) Consider the function v(:c, y) = em(a: sin(y) + ycos(y)) and show that v is harmonic. (d) (6 points) Find a function f : (C > (C that is complex differentiable such that v is the imaginary part of f

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