z = x + iy
f(z) = u(z) + iv(z)
Given Re(f) = u
A) use laplacian to find out if f can be made an analytic function, with suitable choice for v
B) if the answer to A is yes, find v and f'
If the answer to A is no, assume v = 0 and find where (if anywhere) f' exists
C) express f in terms of z, instead of x and y separately
Answer the following:
1. u = x + y
2. u = x^2 + y^2 + 1
Please show steps