Satisfies Cauchy-Riemann equations but not differentiable

[ak123456]

Homework Statement

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

Homework Equations

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 ?

 

[ak123456]

_z is x-iy

 

[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.