imaginary number

A complex number in which the imaginary part is not zero.

American Heritage® Dictionary of the English Language, Fifth Edition. Copyright © 2016 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

imaginary number

(Mathematics) any complex number of the form ib, where i = √–1

Collins English Dictionary – Complete and Unabridged, 12th Edition 2014 © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003, 2006, 2007, 2009, 2011, 2014

imag′inary num′ber

a complex number having its real part equal to zero.

[1905–10]

i·mag·i·nar·y number

(ĭ-măj′ə-nĕr′ē)

A type of complex number in which the multiple of i (the square root of -1) is not equal to zero. Examples of imaginary numbers include 4i and 2 - 3i, but not 3 + 0i (which is just 3). See more at complex number.

The American Heritage® Student Science Dictionary, Second Edition. Copyright © 2014 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

ThesaurusAntonymsRelated WordsSynonymsLegend:

Noun

imaginary number - (mathematics) a number of the form a+bi where a and b are real numbers and i is the square root of -1

complex number, complex quantity, imaginary

math, mathematics, maths - a science (or group of related sciences) dealing with the logic of quantity and shape and arrangement

number - a concept of quantity involving zero and units; "every number has a unique position in the sequence"

complex conjugate - either of two complex numbers whose real parts are identical and whose imaginary parts differ only in sign

real, real number - any rational or irrational number

pure imaginary number - an imaginary number of the form a+bi where a is 0

imaginary part, imaginary part of a complex number - the part of a complex number that has the square root of -1 as a factor

Translations

imaginární číslo

φανταστικός αριθμός

número imaginario

imaginaariluku

nombre imaginaire pur

מספר מרוכב

imaginarni broj

imaginárius számképzetes szám

þvertala

허수

мнимое число

Mentioned in

References in periodicals archive

It was not until around the turn of the 19th century that a graphical representation of imaginary number was realised first by the Norwegian surveyor Caspar Wessel (1799), then by the Swiss born French mathematician John-Robert Argand (1806), the French mathematician Abbee Adrien-Quentin Buee (1806) and the German mathematician Carl Friedrich Gauss (1831).

Imagining complex numbers by generating, interpreting and representing them

Not all brushes with the arcane are necessarily induced onverbal or visual frontiers, defined exclusively through words or images.They can be induced imaginatively, as in "Purgatory, theFilm," or intellectually, as in "Imaginary Number,"the poem that opens the book.

Disassociated selves: Vijay Seshadri's 3 Sections

However, since the serial impedance Z is the serial impedance of an inductance and a capacitance, it will be an inductive impedance when [omega][L'.sub.s] > 1/([omega]w[C'.sub.s]) such that [gamma] be a purely imaginary number supporting propagating waves.

The serial resonant antenna for the large field of view magnetic resonance imaging

Naber carried out the time fractional modification to the Schrodinger equation in analogy with time fractional diffusion equation [19] but included the imaginary number i raised to a fractional power (the fractional degree being the same as the fractional order of the time derivative), implying a sort of the Wick rotation.

Time fractional Schrodinger equation revisited

With respect to Rauscher and Targ's spacetime model, it is true that you can treat the time difference between two events as a pure imaginary number of the form cti.

Correspondence

It is likely all government agencies will be scrutinized closely in an effort to minimize "waste, fraud, and abuse"--a lovely phrase overused by public officials trying to come up with savings they can't really identify but put an imaginary number on for budget purposes.

Positive outcomes

Here, i = [square root of -1] is the imaginary number, [alpha] is the charge- mass ratio defined by

Fundamental elements and interactions of nature: a classical unification theory

An imaginary number i is defined as the square root of minus one.

Meaning and abduction as process-structure: a diagram of reasoning

The square root of minus one, called an imaginary number, is a very real concept that I have used in research articles in mathematics.

P.S.: reader commentary

One day, while dialing an imaginary number, she mysteriously hears the voice of another girl on the other end.

Otsu-Ichi, Calling you

The figures referred to an imaginary number of jobs and additional wealth which a reorganisation of government could bring to the region.

In my view

You have reached an imaginary number. Please rotate your phone 90 degrees and try again.

The message you might want to get across