Using Imaginary NumbersDate: 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/ |
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