## Western Kentucky University

# Imaginary Numbers in Real-World Applications

## Institution

Western Kentucky University

## Faculty Advisor/ Mentor

Bruce Kessler; Stacy Wilson

## Abstract

The concept of imaginary numbers is familiar to most individuals who took Algebra II in high school. However, most people leave that course without ever realizing the usefulness of this concept. Imaginary numbers are by definition an abstract idea, meaning that they do not exist in the real world, yet they can be used to solve real-world problems. As dual majors in engineering and mathematics, we have been exposed to complex numbers (a real number plus an imaginary number) as both an abstract concept and as a useful tool for many tasks performed by engineers on a daily basis. Complex numbers are used to find the characteristics of a circuit, to determine the stability of a control system, to analyze the qualities of both analog and digital signals, and to solve numerous other applications. This poster will show how this inherently non-real concept developed by mathematicians can be used to solve physical problems encountered by engineers in the real world.

Imaginary Numbers in Real-World Applications

The concept of imaginary numbers is familiar to most individuals who took Algebra II in high school. However, most people leave that course without ever realizing the usefulness of this concept. Imaginary numbers are by definition an abstract idea, meaning that they do not exist in the real world, yet they can be used to solve real-world problems. As dual majors in engineering and mathematics, we have been exposed to complex numbers (a real number plus an imaginary number) as both an abstract concept and as a useful tool for many tasks performed by engineers on a daily basis. Complex numbers are used to find the characteristics of a circuit, to determine the stability of a control system, to analyze the qualities of both analog and digital signals, and to solve numerous other applications. This poster will show how this inherently non-real concept developed by mathematicians can be used to solve physical problems encountered by engineers in the real world.