Thread: Conjugate of the derivative...

1. Conjugate of the derivative...

Hi everyone,
I need help with the following:

If $f$ is $C^1$ show that

$\left( \frac{\partial}{\partial z} f \right)^* = \frac{\partial}{\partial z^*} f^*$

where ^ $*$ is the complex conjugate. I am not sure what $f^*$ is so I have no place to start. Any help is greatly appreciated. Thanks

2. If ^* is the complex conjugate, then $f^*$ is the complex conjugate of f..... It may help you to write f(x,y) = u(x,y) + i v(x,y) and then use the facts that $x=\frac{z+z^*}2$ and $y=\frac{z-z^*}2$.

3. Originally Posted by maddas
If ^* is the complex conjugate, then $f^*$ is the complex conjugate of f..... It may help you to write f(x,y) = u(x,y) + i v(x,y) and then use the facts that $x=\frac{z+z^*}2$ and $y=\frac{z-z^*}2$.
Can I always write $f$ in such a form? That was my problem. I will try what you said in the meantime, thanks.

4. Yes, you may. Btw, your name is cool.

5. Originally Posted by maddas
Yes, you may. Btw, your name is cool.
Pretty cool eh
Thanks again