http://img10.imageshack.us/img10/6880/40858143cx2.png

How would I prove this?

Printable View

- Feb 5th 2009, 06:50 PMronaldo_07[SOLVED] Complex Analysis Proof
http://img10.imageshack.us/img10/6880/40858143cx2.png

How would I prove this? - Feb 6th 2009, 09:28 AMThePerfectHacker
Write $\displaystyle f(x+iy) = u(x,y) + iv(x,y)$.

We know that $\displaystyle v(x,y)=0$ by hypothesis.

But, $\displaystyle u_x = v_y \implies u_x = 0 \implies u(x,y) = g(y)$.

And, $\displaystyle u_y = -v_x \implies u_y = 0 \implies u(x,y) = h(x)$.

Therefore, $\displaystyle g,h$ need to be constant functions.

And so $\displaystyle u(x,y) = c$.