Part of the Mathematics glossary:

An imaginary number is a quantity of the form ix, where x is a real number and i is the positive square root of -1.  The term "imaginary" probably originated from the fact that there is no real number z that satisfies the equation z2 = -1.  But imaginary numbers are no less "real" than real numbers.  The quantity i is called the unit imaginary number.  In engineering, it is denoted j, and is known as the j operator.

The unit imaginary number has some intriguing properties.  For example:

(-i)2 = -1
but -i is different from i

i3 = i2i = (-1)i = -i

i4 = i2i2 = (-1)(-1) = 1

i5 = i3i2 = (i3)(-1) = (-i)(-1) = i

in = i(n-4)
when n is a natural number larger than 4

As i is raised to higher natural-number powers, the resultant cycles through four values:  i, -1, -i, and 1 in that order.  No real number behaves like that!

The set I of imaginary numbers consists of the set of all possible products iw, where w is an element of the set R of real numbers.  Therefore, the sets I and R are in one-to-one correspondence.  The sum v + iw of a real number v and an imaginary number iw forms a complex number.  The set C of all complex numbers corresponds one-to-one with the set R ? R of all ordered pairs of real numbers.  The set C also corresponds one-to-one with the points on a geometric plane.

Imaginary and complex numbers are used in engineering, particularly in electronics.   Real numbers denote electrical resistance, imaginary numbers denote reactance, and complex numbers denote impedance.

This was last updated in September 2005
Posted by: Margaret Rouse

Related Terms

Definitions

  • normal distribution

    - A normal distribution is an arrangement of a data set in which most values cluster in the middle of the range and the rest taper off symmetrically toward either end.  A graphical representation of ... (WhatIs.com)

  • zettaflops

    - Zettaflop or (ZFlop) is a processing power of one septillion floating point operations per second (FLOPS). The zetta in zettaflop represents 10 to the 21st power -- 10 multiplied by itself 21 times... (WhatIs.com)

  • mathematical induction

    - Mathematical induction is a a specialized form of deductive reasoning used to prove a fact about all the elements in an infinite set by performing a finite number of steps.  (WhatIs.com)

Glossaries

  • Mathematics

    - Terms related to mathematics, including definitions about logic, algorithms and computations and mathematical terms used in computer science and business.

  • Internet applications

    - This WhatIs.com glossary contains terms related to Internet applications, including definitions about Software as a Service (SaaS) delivery models and words and phrases about web sites, e-commerce ...

Ask a Question About imaginary numberPowered by ITKnowledgeExchange.com

Get answers from your peers on your most technical challenges

Tech TalkComment

Share
Comments

    Results

    Contribute to the conversation

    All fields are required. Comments will appear at the bottom of the article.