In the preceding sections we examined some rudiments of the algebra and geometry of complex numbers. But we have barely scratched the surface of the subject known as complex analysis; the main thrust of our study lies ahead. Our goal in the sections and chapters that follow is to examine functions of a single complex variable z = x + iy and the calculus of these functions.
Before introducing the notion of a function of a complex variable, we need to state some essential definitions and terminology about sets in the complex plane.
Before discussing the concept of functions of a complex ...