1. Introduction to this text

These notes are meant as an introductory exploration of complex numbers. They are structured to be both readable and thorough such that going through them, and doing all of the exercises should put you in a good place for understanding the foundation of this fascinating subject. There is a great deal more that can, and has, been said about complex numbers, so consider this your first journey into this world.

The real work on complex numbers starts in section 3, so section 2 is just getting you thinking about number systems in general and indeed what a number really means. This is a little historical and philosophical aside, but I hope that it will get you thinking about some things which you probably thought you knew before, but maybe hadn't considered all that carefully.

Finally, these notes are a work in progress. There are likely many typos in them, so if you find any, please email jon.shock@gmail.com and we will endeavour to fix it as soon as we can.

Most of all, enjoy!