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

### Real Life Applications of Imaginary Numbers

```
Date: 03/08/98 at 13:25:11
From: Kevin Shah
Subject: Imaginary Numbers

Dr. Math,

I am a sophomore in high school and I am currently studying imaginary
numbers. As an extra assignment, my teacher asked us to find out who
uses imaginary numbers and why. Why are they so important? I tried
looking through your archives and found info on what they are and the
history behind them. But I need to find out who uses them and when do
they use them.

Thanks
```

```
Date: 03/09/98 at 07:43:43
From: Doctor Jerry
Subject: Re: Imaginary Numbers

Hi Kevin,

It would be easier to ask who doesn't use complex numbers. Since
complex numbers are often called "imaginary numbers," they often
become suspect, seen as mathematicians' playthings. This is far, far
from the truth, although apart from my saying this, it is not easy to
prove.

Complex numbers enter into studies of physical phenonomena in ways
that most people can't imagine. There is, for example, a differential
equation, with coefficients like the a, b, and c in the quadratic
formula, that models how electrical circuits or forced spring/damper
systems behave. The movement of the shock absorber of a car as it goes
over a bump is an example of the latter. The behavior of the
differential equations depends upon whether the roots of a certain
quadratic are complex or real. If they are complex, then certain
behaviors can be expected. These are often just the solutions that one
wants.

In modeling the flow of a fluid around various obstacles, like around
a pipe, complex analysis is very valuable for transforming the problem
into a much simpler problem.

When everything from large structures of riveted beams to economic
systems are analyzed for resilience, some very large matrices are used
in the modeling. The matrices have what are called eigenvalues and
eigenvectors. The character of the eigenvalues, whether real or
complex, is important in the analysis of such systems.

In everyday use, industrial and university computers spend some
fraction of their time solving polynomial equations. The roots of such
equations are of interest, whether they are real or complex.

And complex numbers are useful in studying number theory, which is the
study of the positive integers. The techniques in complex analysis
are just one more tool that researchers have.

-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