# Satisfies Cauchy-Riemann equations but not differentiable

1. Apr 21, 2009

### ak123456

1. The problem statement, all variables and given/known data
Let f denote the function defined by
f(z)=
_z^2 /z if z is not 0
0 if z=0
show that f satisfies the Cauchy-Riemann equations at z=0 but that f is not differentiable there

2. Relevant equations

3. The attempt at a solution
it is easily to show the function satisfies Cauchy-Riemann equations
but how to show it is not differentiable
can i show f'(0) does not exist when z tends to 0 ?

2. Apr 21, 2009

### ak123456

_z is x-iy

3. Apr 21, 2009

### eok20

What you need to show is that f'(0) = lim_{h -> 0} ((f(h) - f(0))/h = lim_{h -> 0} _h^2/h^2. does not exist. To show that this limit does not exist, try approaching 0 in two different ways and show you get something different.