Complex maps

This applet demonstrates a number of complex maps w = f(z). By default the identity map f(z) = z is displayed, but other maps can be chosen. The left grid represents the z complex plane (the domain of f), and the right grid represents the w complex plane (the range of f). Moving the mouse around the z plane will cause a pointer to move in the w plane according to whatever complex map was selected.

The spacings in the grids are one unit long; thus both grids have real part and imaginary part ranging from -5 to 5.

Dragging the mouse around on the z plane will trace out a red curve on the z plane, as well as a corresponding curve on the w plane. The "Clear" button will clean the grids.

To get the most out of this applet, try the functions one by one (I recommend starting with the top map and moving downwards), and play with each function until you understand exactly what it does, and why it does it. (Some of the later maps are less intuitive, but do try to make the effort to understand them).

More notes and things to try appear below.

General notes:

With each map, ask yourself the following questions:

Some notes on individual functions:

Previous applet: The Complex Plane

Next applet: Möbius transforms

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