# Thread: Show that u is not part of analytic function

1. ## Show that u is not part of analytic function

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

2. ## Re: Show that u is not part of analytic function

Hey mathsforumhelp.

Are you dealing with a complex function such that u(x,y) is real part and v(x,y) is complex part for an input z = x + iy?

3. ## Re: Show that u is not part of analytic function

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).