Real Life Applications of Imaginary NumbersDate: 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/ |
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