# Complex Analysis Question

• Jul 29th 2009, 03:29 AM
curlyfriesyummy
Complex Analysis Question
I'm having trouble with this showing question.

http://i237.photobucket.com/albums/f...hsQuestion.jpg
Any help would be much appreciated. thanks!
• Jul 29th 2009, 03:46 AM
chisigma
Setting $\displaystyle z= x + i\cdot y$ and $\displaystyle f(z)= u(x,y) + i\cdot v(x,y)$, $\displaystyle f(*)$ is analytic in a region $\displaystyle A$ of the complex plane if and only if in that region is...

$\displaystyle \frac{\partial u}{\partial x}=\frac{\partial v}{\partial y}$

$\displaystyle \frac{\partial u}{\partial y}=- \frac{\partial v}{\partial x}$ (1)

But $\displaystyle f(*)$ is a real function in $\displaystyle A$ so that is $\displaystyle v(z)=0$ and therefore for the (1) is $\displaystyle \frac{\partial u}{\partial x} = \frac{\partial u}{\partial y}=0$...

Kind regards

$\displaystyle \chi$ $\displaystyle \sigma$
• Aug 1st 2009, 03:21 AM
curlyfriesyummy
how did you arise to f(*) is a real function in A so that v(z) = 0 ?