A simple but still interesting example is presented with the complex function [math]g(z)=z^2+az+b[/math].[br]In this GeoGebra activity, The parameters [math]a[/math] and [math]b[/math] are controlled by the complex numbers (points) [b]a[/b] and [b]b[/b] in the domain frame. A circle of radius [math]\delta[/math] controlled by the slider and center at the complex number (point) [math]z_#[/math] is used to locate [b]m[/b] points n the circle where [b]m[/b] is con trolled by another slider. [br][br]The 3-dimensional frame has the mapping diagram for the function visualized using the points on the circles in the domain frame along with the point [math]z_#[/math]. For comparison the graph of an associated real quadratic function is shown in the third 2-dimensional frame.[br][br]Changes can be made by moving [math]z_#[/math], [b]m[/b], [b]a, [/b]b or [math]\delta[/math], or by entering a new complex function using parameters [b]a[/b] or [b]b[/b]. This example can be removed from sight in the activity by unchecking the box labelled "Show function g with parameters a and b".[br][br]A more subtle example can be shown by checking the box labelled [br]"Show function h with parameters a, b, c and d".[br]This will show the function [math]h(z)=\frac{az+b}{cz+d}[/math] using parameters [b]a,b,c,[/b] and [b]d[/b] controlled by the appropriate complex numbers (points) in the domain frame. The other two frames are as with the quadratic example.[br]Again the diagram can be controlled by changing the parameters. [br]