Using Imaginary Numbers

Date: 05/04/2001 at 22:44:19
From: Srini
Subject: Imaginary Numbers

Hi,

Where do we use imaginary numbers in the real world?

Thanks in advance,
Srini.K

Date: 05/04/2001 at 23:39:16
From: Doctor Douglas
Subject: Re: Imaginary Numbers

Hi Srini, and thanks for writing.

One of the most familiar examples where we use imaginary numbers, or 
"complex numbers" as they are sometimes called, is from electrical 
engineering, where imaginary numbers are used to keep track of the 
amplitude and phase of an electrical oscillation, such as an audio 
signal, or the electrical voltage and current that power electrical 
appliances.

Check out the following Web pages on our site, which talk briefly
about the electrical example as well as some others:

  Imaginary Numbers in Electricity
  http://mathforum.org/dr.math/problems/munoz7.31.98.html   

  Real Life Applications of Imaginary Numbers
  http://mathforum.org/dr.math/problems/shah3.8.98.html   

  Applications of Complex Numbers
  http://mathforum.org/dr.math/problems/stewart12.6.97.html   

  Applications of Imaginary Numbers
  http://mathforum.org/dr.math/problems/zakrzewski10.14.97.html   

  Imaginary Numbers
  http://mathforum.org/dr.math/problems/matt02.28.99.html   

Closely related to the electrical engineering example is the use of 
complex numbers in signal processing, which has applications to 
telecommunications (cellular phone), radar (which assists the
navigation of airplanes), and even biology (in the analysis of firing 
events from neurons in the brain).

Another important application of complex numbers is their use in a 
field of physics called quantum mechanics. Although quantum mechanics
is not an everyday subject, it is extremely important in many common 
applications with which we are familiar. Imaginary (complex) numbers
help form the descriptions of electronic states in materials (which 
lead to applications in optics - fluorescent and incandescent lights 
and CCD cameras, even the description of polarization for polarized 
sunglasses),  electronics (transistors and other semiconductor 
devices, as well as magnetism, which has applications to magnetic disk 
drives and other storage devices), and chemistry (the covalent bonding 
between atoms).  

I hope this gives you a few real-world applications where imaginary 
numbers are used in science and engineering. Please write back if you 
have further questions.  

- Doctor Douglas, The Math Forum
  http://mathforum.org/dr.math/