Associated Topics || Dr. Math Home || Search Dr. Math

Applications of Complex Numbers

```
Date: 12/06/97 at 23:23:17
From: David Stewart
Subject: Applications of complex #s in society today

Dear Dr.Math,

I am a sophomore in high school in Dallas, TX. In my Algebra 2 class,
my teacher assigned a project for us in which we must find some common
applications of complex numbers, like the square root of negative one,
in our society today. My teacher already gave me one example, which is
that it is used to describe electrical currents. I was wondering if
you know of any other uses of imaginary numbers.

Dave
```

```
Date: 12/07/97 at 08:32:26
From: Doctor Jerry
Subject: Re: Applications of complex #s in society today

Hi David,

Engineers use complex numbers in analyzing stresses and strains on
beams and in studying resonance phenomena in structures as different
as tall buildings and suspension bridges. The complex numbers come up
when they look for the eigenvalues and eigenvectors of a matrix. The
eigenvalues are roots of a certain polynomial equation associated with
a matrix. The matrices may be quite large, maybe 10000 by 10000, and
the associated polynomials are of very high degree.

Complex numbers are used in studying the flow of fluids around
obstacles, such as the flow around a pipe.

Mathematicians use complex numbers in many ways, but one way is in
studying infinite series, like

e^z = 1+z+z^2/2!+z^3/3!+z^4/4!+...,

where z = x+i*y is a complex variable. This is a more "natural"
environment to study series than on the real line. You might be
interested in a fact that comes from the above series: it is that

e^(i*pi) = -1.

This brief equation relates 4 of the most fundamental constants in
mathematics, e, i, pi, and 1. Your calculator may be able to handle
complex numbers. You might be able to check that

e^(i*t) = cos(t)+i*sin(t),

from which the earlier result follows.  Just let t = pi.

-Doctor Jerry,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
High School Imaginary/Complex Numbers

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search