Juan Carlos Ponce Campuzano

The study of complex analysis is important for students in engineering and the physical sciences and is a central subject in mathematics. In addition to being mathematically elegant, complex analysis provides powerful tools for solving problems that are either very difficult or virtually impossible to solve in any other way.

In this book you will find examples, problems and applets that allow you to explore complex analysis by using the visual interactive power of the computer (or tablet).

Ready to get started? Skip ahead to the Table of Contents.


This book is an interactive introduction to the theory and applications of complex functions from a visual point of view. However, it does not cover all the topics of a standard course. In fact, it is a collection of selected topics and interactive applets that can be used as a supplementary learning resource by anyone interested in learning this fascinating branch of mathematics.

Some of the topics covered here are basic arithmetic of complex numbers, complex functions, domain coloring, analytic landscapes and some applications of conformal mappings.

What distinguishes this book from other texts in the first instance is the use of interactive applets that allow you to explore properties of complex numbers geometrically and analyze complex functions by using different techniques to visualize them. For the design of applets I used the following open-source softwares:



Of course, no project such as this can be free from errors and incompleteness. If you find applets that don't run correctly, or the examples that aren't explained quite right, or a typo, please report them at this project's GitHub repository. Thanks for your help!


The design of this book is based upon the fantastic book Collision Detection written by Jeffrey Thompson. If you want to learn about the algorithms behind collisions using basic geometrical shapes, you should check it!


OK, let's begin! Click the link at the bottom the page, or the arrows at the top, to move to the next chapter. The Complex Analysis link at the top will take you back to the Table of Contents.

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