Complex Analysis: Lecture 1: complex numbers

Here we discuss a few possible models for the complex numbers. Our choice, for convenience, is that the complex numbers are the plane with the Gauss multiplication. That said, we use the notation a+ib in almost everything which follows. Complex conjugation is defined and connections to the real and imaginary part maps are given. We also discuss why every nonzero complex number has a multiplicative inverse (but, I stop short of mentioning that makes C a field, more on that next time). We are  about half-way through section 1.1 of http://www.supermath.info/GuideToGame... also the course page is at http://www.supermath.info/Complex.html