Solve the analytic functions. Please show every steps. a. Show v(x,y) = x3-3xy2 is a harmonic function, and find the analytic function f(z) = u(x,y) + i v(x,y). b. Given the imaginary part v(x,y) = sinh(x)cos(y) and f(2i) = 0, find f(z).

Is the function u = x3 – 3xy? harmonic? If your answer is yes, find a corresponding analytic function. NOTE: If the function is harmonic, use c as the arbitrary constant. If the function is not harmonic, indicate that using the checkbox. f(z) = The function is not harmonic