Hi Here there are two graphs for two functions from $R^2\mapsto R$.

Is there similar graph for the absolute value of a complex variable function $f:C\mapsto C$ that has the same point (like saddle point or transition). I know some functions that have the point $(x,y,|f(x+iy)|)$ on that such that in one direction it is maximum, and in the other direction it is minimum.

My question here is that: is there any such point such that in one direction it is maximum (or minimum) but in the other direction it is not maximum nor minimum (similar to $(0,0)$ in $y=x^3$ in the real case).

Thanks