# Cauchy Riemann Equations (basic doubt)

## Main Question or Discussion Point

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.

HallsofIvy
$$\frac{g(x,y)}{\partial x}= \frac{\partial g(x,y)}{\partial y}= 0$$