ABSTRACT
There are numerous operations in mathematics involving real variables whose outcome is a number that does not belong to the real number system. The simplest of these involves finding the square root of −1, denoted by i = − 1. https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429187483/fa12fecb-bf1b-4d64-928e-c1b02366a23e/content/inequ4_143_1.tif"/> The first part of this chapter is devoted to developing a general understanding of complex numbers. The study of complex numbers is the study of numbers that can be represented in the form a + ib, where a and b are real numbers. The number a is called the real part of the complex number, and the number b is called the imaginary part. Complex numbers provide the generalization of the real number system necessary to ensure that all numbers produced by mathematical operations are included in what is called the field of complex numbers. As would be expected, a real number is a special case of a complex number in which the imaginary part is zero.
