Imaginary Numbers

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.