Fundamentals of University Mathematics, 3rd Edition

Chapter 6

Complex Numbers

As we have seen in Section 3.3, there are some polynomials which have no real roots. For example, there is no real number x which satisfies x² + 1 = 0. The aim of this chapter is to introduce and study a number system —the complex numbers—in which this, and all other quadratic equations can be solved. The reader should see this as a natural step in the evolution of number systems outlined in the introduction the Chapter 1 and amplified in the paragraph following Problem 1.1.2.

In the introduction to Chapter 1, we indicated that everything would be based on real numbers. In keeping with this philosophy, we define a complex ...