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Show that u is not part of analytic function

Attachment 25244

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 http://s3.amazonaws.com/answer-board...8797178215.gif0 -> it's not the real part of an analytic function

Is the answer correct.....

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?

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).