Imaginary Numbers in Real LifeDate: 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 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. From the Dr. Math archives, see also: 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/ |
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