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

SearchCompliance

SearchSecurity

  • cyber attack

    A cyber attack is any attempt to gain unauthorized access to a computer, computing system or computer network with the intent to ...

  • backdoor (computing)

    A backdoor is a means to access a computer system or encrypted data that bypasses the system's customary security mechanisms.

  • post-quantum cryptography

    Post-quantum cryptography, also called quantum encryption, is the development of cryptographic systems for classical computers ...

SearchHealthIT

SearchDisasterRecovery

  • risk mitigation

    Risk mitigation is a strategy to prepare for and lessen the effects of threats faced by a business.

  • call tree

    A call tree is a layered hierarchical communication model that is used to notify specific individuals of an event and coordinate ...

  • Disaster Recovery as a Service (DRaaS)

    Disaster recovery as a service (DRaaS) is the replication and hosting of physical or virtual servers by a third party to provide ...

SearchStorage

  • cloud SLA (cloud service-level agreement)

    A cloud SLA (cloud service-level agreement) is an agreement between a cloud service provider and a customer that ensures a ...

  • NOR flash memory

    NOR flash memory is one of two types of non-volatile storage technologies.

  • RAM (Random Access Memory)

    RAM (Random Access Memory) is the hardware in a computing device where the operating system (OS), application programs and data ...

Close