## Cauchy Riemann Equations (basic doubt)

Lets say we have a function of a complex variable z , f(z).

I read that for the function to be differentiable at a point z0 , the CR equations are a necessary condition but not a sufficient condition.

Can someone give me an example where the CR equations hold but the function is not differentiable at that point , thus justifying that the CR equations holding true aren't sufficient test.

I am unable to visualise.

 PhysOrg.com science news on PhysOrg.com >> Heat-related deaths in Manhattan projected to rise>> Dire outlook despite global warming 'pause': study>> Sea level influenced tropical climate during the last ice age
 Recognitions: Gold Member Science Advisor Staff Emeritus Let g(x, y)= 1 if xy is not 0, 0 if xy= 0 and let f(z)= g(x,y)(1+ i)= g(x, y)+ ig(x,y) where z= x+ iy. Then $$\frac{g(x,y)}{\partial x}= \frac{\partial g(x,y)}{\partial y}= 0$$ for (x,y)= (0, 0) so the Riemann-Cauchy equations are satisfied there but the function is not even continuous at (0, 0).
 Thanks.Doubt resolved.

 Tags cauchy riemann