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Please show all steps, thank you: Problem C: Does there exist an analytic function f(z) in...

Please show all steps, thank you:

Problem C: Does there exist an analytic function f(z) in some domain D with the real part u(x,y)=x^2+y^2?

Problem D: Is the function f(z)=(x-iy)^2 analytic in any domain in C? Are the real part u(x,y) and the imaginary pary v(x,y) harmonic in C? Are u and v harmonic conjugates of each other in any domain?

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