# Math Help - Complex Analysis Question

1. ## Complex Analysis Question

I'm having trouble with this showing question.

Any help would be much appreciated. thanks!

2. Setting $z= x + i\cdot y$ and $f(z)= u(x,y) + i\cdot v(x,y)$, $f(*)$ is analytic in a region $A$ of the complex plane if and only if in that region is...

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

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

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

Kind regards

$\chi$ $\sigma$

3. how did you arise to f(*) is a real function in A so that v(z) = 0 ?