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


[link text](http://postimage.org/image/v2ig8ycx7)


[link text](http://postimage.org/image/57zgroy4t)



graph of the size of a complex function
For any nonconstant analytic function $f$, if $f'(p) = 0$ but $f(p)$ and $f''(p)$ are nonzero, then the graph of $|f(z)|$ will have a saddle point at $p$.


