Associated Topics || Dr. Math Home || Search Dr. Math

### 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?

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/
```
Associated Topics:
High School Imaginary/Complex Numbers
High School Physics/Chemistry

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search