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### Imaginary Numbers

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Date: 02/28/99 at 19:32:31
From: Matt Mooney
Subject: Imaginary numbers

I would really appreciate it if you could tell me what jobs and
professions use imaginary numbers. I do not see where they would be
used.

Thanks a lot.
```

```
Date: 03/01/99 at 22:59:11
From: Doctor Tom
Subject: Re: Imaginary numbers

Well, mathematicians use them of course, but that is probably not what
you were looking for.

The best answer for a practical application is by electrical engineers.
With direct current the equation that relates voltage = V, current = I,
and resistance = R, is simple: V = IR. But with alternating current, it
no longer holds. You have to take into account more than just the
resistance; you have to take into account impedence. With direct
current, a capacitor has infinite resistance, and a coil (a pure
inductor) has zero resistance. Yet alternating current can "flow"
through a capacitor, and is impeded by a coil.

If you replace the R in the formula above by "impedence," it is still
true for alternating current, but the only reasonable way to make the
other formulae for combination of circuit elements work is to consider
impedence to be a complex number (that is, a number with both real and
imaginary part).

Also, anyone who solves differential equations involving wavelike
(sinusoidal) functions uses complex variables to get the answer in the
fastest possible way. A huge number of differential equations that
apply to the real world of engineering have this property.

- Doctor Tom, The Math Forum
http://mathforum.org/dr.math/

```

```
Date: 10/07/2009 at 16:14:01
From: Eric
Subject: real use of imaginary numbers

In reading the responses of where imaginary numbers are used in the
real world, I'd like to add my own.

I am an electrical engineer.  The sinusoids that are used to
describe a three phase electrical system are in time-displacement
with one another. In my opinion, "imaginary" numbers could also be
called "phase" numbers, or "time-displacement" numbers because we
represent the time difference between the sinusoids as a distance
in the imaginary direction.

So, in short, imaginary numbers allow us to treat time as a
distance and make the equations much easier to deal with.

Eric Stromberg, P.E.
Stromberg Engineering, Inc.

```
Associated Topics:
High School Physics/Chemistry
Middle School Number Sense/About Numbers

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