Applications of Complex NumbersDate: 12/06/97 at 23:23:17 From: David Stewart Subject: Applications of complex #s in society today Dear Dr.Math, I am a sophomore in high school in Dallas, TX. In my Algebra 2 class, my teacher assigned a project for us in which we must find some common applications of complex numbers, like the square root of negative one, in our society today. My teacher already gave me one example, which is that it is used to describe electrical currents. I was wondering if you know of any other uses of imaginary numbers. Dave Date: 12/07/97 at 08:32:26 From: Doctor Jerry Subject: Re: Applications of complex #s in society today Hi David, Engineers use complex numbers in analyzing stresses and strains on beams and in studying resonance phenomena in structures as different as tall buildings and suspension bridges. The complex numbers come up when they look for the eigenvalues and eigenvectors of a matrix. The eigenvalues are roots of a certain polynomial equation associated with a matrix. The matrices may be quite large, maybe 10000 by 10000, and the associated polynomials are of very high degree. Complex numbers are used in studying the flow of fluids around obstacles, such as the flow around a pipe. Mathematicians use complex numbers in many ways, but one way is in studying infinite series, like e^z = 1+z+z^2/2!+z^3/3!+z^4/4!+..., where z = x+i*y is a complex variable. This is a more "natural" environment to study series than on the real line. You might be interested in a fact that comes from the above series: it is that e^(i*pi) = -1. This brief equation relates 4 of the most fundamental constants in mathematics, e, i, pi, and 1. Your calculator may be able to handle complex numbers. You might be able to check that e^(i*t) = cos(t)+i*sin(t), from which the earlier result follows. Just let t = pi. -Doctor Jerry, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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