# Complex numbers¶

## Using SAGE for complex numbers¶

This chapter tells you how to use the free and Open-Source SAGE mathematics software for studying complex numbers.

To use SAGE, you first need to start the SAGE program on your computer. You should have already installed SAGE on your computer (if not, for instructions on how to install SAGE, see the SAGE Installation Guide).

This booklet assumes that the reader has some basic knowledge of complex numbers, and the principal focus of the booklet is not to explain complex numbers, but rather how to study complex numbers using SAGE.

If you are new to complex numbers, and want to learn more about any of the concepts presented here, I would highly recommend the Open University book “Complex numbers” (product code MS221 chapter D1), available second-hand from from the Open University Book Search.

## Adding, subtracting, multiplying and dividing complex numbers¶

Since Pythagoras, we know that .

In SAGE, we can use the symbol *i* in complex numbers, where:

and a typical complex number *z* has the form:

where *a* and *b* are real numbers.

## Links and Further Reading¶

Some links are included here for further reading.

For background reading on complex numbers, I would recommend the Open University book “Complex numbers” (product code MS221 chapter D1), available second-hand from from the Open University Book Search.

For an in-depth introduction to SAGE, see the SAGE documentation website.

## Acknowledgements¶

Thank you to Sphinx, http://sphinx.pocoo.org, used to create this document, and github, https://github.com/, used to store different versions of the document as I was writing it, and readthedocs, http://readthedocs.org/, used to build and distribute this document.

Many of the examples in this document have been inspired by examples in the excellent Open University book “Complex numbers” (product code MS221 chapter D1), available second-hand from from the Open University Book Search.

## Contact¶

I will be grateful if you will send me (Avril Coghlan) corrections or suggestions for improvements to my email address a.coghlan@ucc.ie

## License¶

The content in this book is licensed under a Creative Commons Attribution 3.0 License.