Answer u(x,y) is the real part of an analytic function if and only if:d^2u/dx^2 + d^2u/dy^2 = 0 But for u(x,y) = x^2+y^2 we have: d^2u/dx^2 = 2 and d^2u/dy^2 = 2 Thus: d^2u/dx^2 + d^2u/dy^2 = 4 0 -> it's not the real part of an analytic function
Is the answer correct.....
Yes, your answer and reasoning are correct. That suffices to prove that u can't be the real part of an analytic function (given the presumed meanings as chiro asked about).