ABSTRACT
Complex numbers play a fundamental role in many areas of physics and engineering. They express information about both magnitude and phase in a very simple way. They are central to understanding Fourier transforms (Chapter 15), and it is worth the effort to become fluent in using them. In treating AC circuits, they handle capacitances and inductances in a neat, compact way. The phasor diagrams of the previous two chapters are in fact graphical representations of complex numbers. Usually it is easier to handle circuit problems algebraically than with diagrams, so this chapter will develop and illustrate the algebra. First, we review the pure mathematics; then we apply it to AC circuits.
