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, 05:10 PMnankorShowing 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, 05:46 PMTheEmptySet
do you mean

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

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

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

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

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