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