# imaginary number

(redirected from Imaginary axis)
Also found in: Thesaurus, Encyclopedia.
Related to Imaginary axis: complex number

## imaginary number

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

## imaginary number

n
(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

n.
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.
ThesaurusAntonymsRelated WordsSynonymsLegend:
 Noun 1 imaginary number - (mathematics) a number of the form a+bi where a and b are real numbers and i is the square root of -1math, mathematics, maths - a science (or group of related sciences) dealing with the logic of quantity and shape and arrangementnumber - 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 signreal, real number - any rational or irrational numberpure imaginary number - an imaginary number of the form a+bi where a is 0imaginary part, imaginary part of a complex number - the part of a complex number that has the square root of -1 as a factor
Based on WordNet 3.0, Farlex clipart collection. © 2003-2012 Princeton University, Farlex Inc.
Translations
imaginární číslo
número imaginario
imaginaariluku
nombre imaginaire pur
מספר מרוכב
imaginarni broj
imaginárius számképzetes szám
þvertala
허수
References in periodicals archive ?
On it, the horizontal axis is called the real axis and the perpendicular vertical axis is called the imaginary axis. (Subsequently, it was not until around the turn of the 20th century that they were used to understand a very practical problem: electricity in the form of alternating current, AC).
The traditional political analysis, the one which divides the parties on an imaginary axis from left to the right and explains most democratic phenomena by reference to the dynamic of the sociological and political parties, is outdated for a long time.
in which [mathematical expression not reproducible] can be any measurable Hermitian-valued function defined on the imaginary axis and the superscript * denotes the complex conjugate transpose.
Since the system is undamped, all the eigenvalues lie on the imaginary axis in the precritical phase, that is, when the value of the force is less than the critical one; namely, [lambda]= i[omega].
Moreover, the eigenvalues of (6) cross imaginary axis in the same direction as the eigenvalues of (8).
(2) The z and p of the lag controller are kept as close to the imaginary axis as possible to avoid shaping the root locus and the transients.
Moreover, if [gamma] is a cofinite Fuchsian group, then [??] = <[sigma], [GAMMA]> is a reflection group and [??] = <[tau], [GAMMA]> is a Coxeter group, where [sigma] is the reflection in the imaginary axis and [tau] is the linear operator represented by the matrix [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], and both groups contain [GAMMA] as a subgroup of index two.
Throughout Budapest, in particular during tete-a-tetes, Yeoman breaks the 180-degree rule of filmmaking, which says that the camera shouldn't cross an imaginary axis that connects two conversing characters.
We have shown that pairs of eigenvalues cross the imaginary axis as t passes through certain critical values.
Note that the application of this function enables a matrix to be decomposed into two components whose spectra lie on opposite sides of the imaginary axis. The matrix sign function is a valuable tool for the numerical solution of Sylvester and Lyapunov matrix equations (see, e.g., [8]).
The first part follows noting that the equilibrium [P.sub.*] is locally asymptotically stable when [tau] = 0 and so its stability can only be lost if eigenvalues cross the imaginary axis from left to right.
Let us, as Higham considered in the fifth Chapter of [6], assume throughout this paper that the matrix A [member of] [C.sup.nxn] has no eigenvalues on the imaginary axis. This assumption implies that the matrix sign function,

Site: Follow: Share:
Open / Close