7 - COMPLEX NUMBERS

Abstract

This chapter discusses the complex numbers. It is a shortcoming of the real number system that not every polynomial equation has a real root. The new number system, called the complex number system, consists of all formal expressions, a + bi, where a and b are real numbers. In the complex number system, all real numbers, even negative numbers, have square roots. Every quadratic polynomial with real or complex coefficients has complex zeros. However, there are numerical methods for approximating zeros to any degree of accuracy; some are well suited for computers. The complex number system contains a subsystem that can be identified with the real number system. The complex number system is an extension of the real number system, and its arithmetic is consistent with that of the real number system.