Browse Definitions:
Definition

imaginary number

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

Start the conversation

Send me notifications when other members comment.

By submitting you agree to receive email from TechTarget and its partners. If you reside outside of the United States, you consent to having your personal data transferred to and processed in the United States. Privacy

Please create a username to comment.

-ADS BY GOOGLE

File Extensions and File Formats

SearchCompliance

  • smart contract

    A smart contract, also known as a cryptocontract, is a computer program that directly controls the transfer of digital currencies...

  • risk map (risk heat map)

    A risk map, also known as a risk heat map, is a data visualization tool for communicating specific risks an organization faces. A...

  • internal audit (IA)

    An internal audit (IA) is an organizational initiative to monitor and analyze its own business operations in order to determine ...

SearchSecurity

SearchHealthIT

SearchDisasterRecovery

  • incident management plan (IMP)

    An incident management plan (IMP), sometimes called an incident response plan or emergency management plan, is a document that ...

  • crisis communication

    Crisis communication is a method of corresponding with people and organizations during a disruptive event to provide them with ...

  • Zerto

    Zerto is a storage software vendor that specializes in enterprise-class business continuity and disaster recovery in virtual and ...

SearchStorage

  • network-attached storage (NAS)

    Network-attached storage (NAS) is dedicated file storage that enables multiple users and heterogeneous client devices to retrieve...

  • SSD write cycle

    An SSD write cycle is the process of programming data to a NAND flash memory chip in a solid-state storage device.

  • data storage

    Data storage is the collective methods and technologies that capture and retain digital information on electromagnetic, optical ...

Close