Imaginary NumbersDate: 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. |
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