Mapping Diagrams: Complex Analysis -functions with complex parameters. circles
A simple but still interesting example is presented with the complex function .
In this GeoGebra activity, The parameters and are controlled by the complex numbers (points) a and b in the domain frame. A circle of radius controlled by the slider and center at the complex number (point) is used to locate m points n the circle where m is con trolled by another slider.
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 . For comparison the graph of an associated real quadratic function is shown in the third 2-dimensional frame.
Changes can be made by moving , m, a, b or , or by entering a new complex function using parameters a or b. This example can be removed from sight in the activity by unchecking the box labelled "Show function g with parameters a and b".
A more subtle example can be shown by checking the box labelled
"Show function h with parameters a, b, c and d".
This will show the function using parameters a,b,c, and d controlled by the appropriate complex numbers (points) in the domain frame. The other two frames are as with the quadratic example.
Again the diagram can be controlled by changing the parameters.