# complex number

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Related to Complex numbers: Imaginary numbers

## complex number

n.
Any number of the form a + bi, where a and b are real numbers and i is an imaginary number whose square equals -1.

## complex number

n
(Mathematics) any number of the form a + ib, where a and b are real numbers and i = √–1. See number1

## com′plex num′ber

n.
a mathematical expression (a + bi) in which a and b are real numbers and i2=−1.
[1825–35]

## com·plex number

(kŏm′plĕks′)
A number that can be expressed in terms of i (the square root of -1). Mathematically, such a number can be written a + bi, where a and b are real numbers. An example is 4 + 5i.
ThesaurusAntonymsRelated WordsSynonymsLegend:
 Noun 1 complex 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
Translations
komplexní číslo
kompleksa nombro
kompleksiluku
מספר מרוכב
kompleksni broj
komplex szám
tvinntala
numero complesso
복소수
komplekst tall
komplexa tal
karmaşık sayılar
References in periodicals archive ?
Gauss had shown that complex numbers could be treated as though they were points on a plane, and that each could be represented by two numbers.
They illustrate the theory with many examples, including matrix groups with entries in the field of real or complex numbers, or other locally compact fields such as p-adic field, isometry groups of various metric spaces, and discrete groups themselves.
Students studying a mathematics specialism as a part of the Victorian VCE (Specialist Mathematics, 2010), HSC in NSW (Mathematics Extension in NSW, 1997) or Queensland QCE (Mathematics C, 2009) will be familiar with de Moivre's theorem and its applications to complex numbers (see the short discourse by Bardell (2014) for further details).
These later sections consider complex numbers, four-dimensional algebra and geometry, constructivist criticisms of math, hyperreal and surreal numbers.
Quaternions were invented by Sir William Rowan Hamilton as an extension to the complex numbers.
Writing for the interested layman, Allday (physics, Royal Hospital School, UK) explains the theory of quantum physics, endeavoring to keep the mathematics to early undergraduate-level algebra and trigonometry (although some discussion of complex numbers and matrices was found to be necessary).
The text starts with an introduction to complex numbers and leads the reader in topics such as Hilbert spaces, complex analysis in several variables, Compact integral operators, and gives some positivity conditions for real-valued functions.
Included are the creation of calculus by Isaac Newton and Gottfried Leibniz, Leonhard Euler's explanation of complex numbers and exponential functions, and Evariste Galois' treatise on algebra and group theory.
Linear algebra, complex numbers, differential equations, and Fourier transformation are used as bases for the analysis, and each chapter ends with problems.
CHAPTER 8 Complex Numbers, Polar Coordinates, and Parametric Equations
He considers infinite series and products in the setting of complex numbers, so complex numbers appear throughout, and he defines elementary functions as functions of a complex variable.
A routine application of Equation (1) will furnish the desired roots, but it gives no indication of the location of these roots if the result contains complex numbers.

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