# Complex Numbers

This book is a study guide for the set of complex numbers and basic operations on complex numbers. The imaginary unit i and the complex numbers are defined. Plotting numbers on the complex plane and representing complex numbers as vectors is illustrated. The operations covered include addition, subtraction, multiplication, division, reciprocals, squares, and absolute value of complex numbers. The whole number powers of the imaginary unit are also explored. Addition, subtraction, and absolute value of complex numbers is also illustrated by vectors on the complex plane. Each topic includes solved examples and practice exercises. A practice test and answers to exercises are included.

This book is ideal for upper level high school students and college students that are enrolled in college level algebra courses or need to review the concepts involved with complex numbers.

## An Introduction to Complex Numbers

This book explains how the set of real numbers and the real number line is enlarged to include further numbers called imaginary numbers and complex numbers. The set of complex numbers requires a two dimensional plane that contains the real number line. We then show the basic operations of addition, subtraction, multiplication, and division of complex numbers. The properties and basic algorithms of real numbers are consistent with the set of complex numbers and are incorporated in this text. Exponents and absolute value are also covered. Complex numbers are useful in a variety of engineering applications, especially alternating current and circuit analysis.

The set of complex numbers is a natural extension of the real numbers. The complex numbers enable us to solve polynomials and other types of equations that have no real number solutions. This book is divided into two main sections. Section one introduces the complex numbers as a set and how the numbers are represented graphically. Section two shows how the basic arithmetic operations are defined in the complex numbers and how algebraic algorithms are consistent with the set of real numbers. After completing this text, the reader will be proficient with the complex number set, how complex numbers are graphed, and the basic operations of complex number arithmetic.