In this section we will define what we mean by a complex func- tion. We will then generalise the definitions of the exponential, sine and cosine functions using complex power series. To deal with complex power series we define the notions of conver- gent and absolutely convergent, and see how to use the ratio test from real analysis to determine convergence and radius of convergence for these complex series. We start by defining domains in the complex plane. This requires the prelimary definition
