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### Imaginary Numbers in Real Life

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Date: 11/20/2001 at 21:58:34
From: Chris Valentine
Subject: When in real life would you use and an imaginary number (i)?

Dr. Math -

In our Accelerated Algebra II class, we have been discussing when we
would use the imaginary number "i" in real life. My teacher
recommended you for the answer. I hope you can help us. Thank you!

Sincerely,
Chris Valentine
```

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Date: 11/21/2001 at 08:01:48
From: Doctor Jerry
Subject: Re: When in real life would you use and an imaginary number
(i)?

Hi Chris,

It would be easier to say 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 from
the truth, although not easy to prove. If you were to spend some time
in a university library looking through physics, engineering, and
chemistry journals or through books in these disciplies, you would
find many applications of complex numbers. But this is difficult,
since the uses are often buried under a lot of terminology.

Complex numbers enter into studies of physical phenonomena in
unexpected ways. There is, for example, a differential equation with
coefficients like a, b, and c in the quadratic formula, which models
how electrical circuits or forced spring/damper systems behave. A car
equipped with shock absorbers and going 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 to transforming the problem
to a much simpler problem.

When economic systems or large structures of beams put together with
rivets are analyzed for strength, some very large matrices are used in
the modeling. The eigenvalues and eigenvectors of these matrices are
important in the analysis of such systems. The character of the
eigenvalues, whether real or complex, determines the behavior of the
system. For example, will the structure resonate under certain loads.
In everyday use, industrial and university computers spend a
significant portion of their time solving polynomial equations. The
roots of such equations are of interest, whether they are real or
complex.

Applications of Imaginary Numbers
http://mathforum.org/dr.math/problems/zakrzewski10.14.97.html

Real Life Applications of Imaginary Numbers
http://mathforum.org/dr.math/problems/shah3.8.98.html

Using Imaginary Numbers
http://mathforum.org/dr.math/problems/srini.05.04.01.html

Uses of Imaginary Numbers
http://mathforum.org/dr.math/problems/boyer3.24.97.html

- Doctor Jerry, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Imaginary/Complex Numbers

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