Complex Plane Transformations

Investigate complex plane transformations of the form w=f(z).

If you have ever studied complex analysis and in particular, complex plane transformations of the form w=f(z), then this application may be of interest.

You can define constants and expressions using a rich set of mathematical functions and then apply a transformation to both a single value of z and to a grid of values on the complex plane. This allows you to visualise the effect of your transformation on the complex plane. For instance, you may know that a particular transformation rotates and scales the plane, but this application will allow you to actually see it happening. You can apply the transformation once or apply it over and over again if appropriate.

Real and complex plots provide additional visual feedback as you apply a transformation. The real plot can display either Re(z), Im(z), Mod(z) or Arg(z). The complex plot displays values of z on an Argand diagram. You can change the real plot mode at any point, allowing you to clearly see how the values are changing over time. The plots make this application an invaluable tool for understanding the effect a transformation has on particular values of z.

The powerful complex number expression evaluator means the application can also be used as a general purpose, albeit somewhat unconventional, calculator.

Everything you enter on up to 10 worksheets is automatically saved as you go along, so everything looks exactly the same next time you launch the application. This means you can define up to 10 different transformations and then recall them for class demonstrations or discussions.

Finally, you are not left alone to figure out how the application works. There is a brief user guide, help with expressions and several detailed examples you can work through.

We hope you enjoy using this application and learn at least a little bit more about this fascinating area of mathematics.