# Showing that f'(z) does not exist at any point (complex analysis)

• May 4th 2009, 06:10 PM
nankor
Showing that f'(z) does not exist at any point (complex analysis)
I am having a hard time showing that f'(z) does not exist at any point for

f(z)=z-z(conjugate)

An explanation would be greatly appreciated,

Thanks.
• May 4th 2009, 06:46 PM
TheEmptySet
Quote:

Originally Posted by nankor
I am having a hard time showing that f'(z) does not exist at any point for

f(z)=z-z(conjugate)

An explanation would be greatly appreciated,

Thanks.

do you mean

$f(z)=z-\bar z=x+iy-(x-iy)=2yi$

so $u(x,y)=0 \mbox{ and } v(x,y)=2y$

$\frac{\partial u }{\partial x} =0$

$\frac{\partial v}{\partial y}=2$

So $f(z)$ does not satisfy the cauchy-reimann equation at any point so it is not diff at any point