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Imaginary Numbers in Real Life


Date: 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/   
    
Associated Topics:
High School Imaginary/Complex Numbers

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