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# complex number

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

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Any number consisting of both real numbers and imaginary numbers.

It has the form a + bi, where a and b are real numbers and i = -1; a is called the real part and bi the imaginary part. Because a or b can equal 0, any real or imaginary number is also a complex number. Invented as an extension of the real numbers so that certain algebraic equations such as x2 + 1 = 0 would have solutions, the complex numbers form an algebraic field, meaning that they obey the commutative law and the associative law (with respect to addition and multiplication), as well as certain other rules in much the same way real numbers do (see field theory).

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number of the form x + yi, in which x and y are real numbers and i is the imaginary unit such that i2 = -1. See numerals and numeral systems.

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Universalium. 2010.

### Look at other dictionaries:

• Complex number — Complex Com plex (k[o^]m pl[e^]ks), a. [L. complexus, p. p. of complecti to entwine around, comprise; com + plectere to twist, akin to plicare to fold. See {Plait}, n.] 1. Composed of two or more parts; composite; not simple; as, a complex being; …   The Collaborative International Dictionary of English

• complex number — n. any number expressed as a + bi, where a and b are real numbers and i is the imaginary unit, √P1: if b is zero it is a real number, but if b is not zero it is an imaginary number …   English World dictionary

• complex number — ► NOUN Mathematics ▪ a number containing both a real and an imaginary part …   English terms dictionary

• Complex number — A complex number can be visually represented as a pair of numbers forming a vector on a diagram called an Argand diagram, representing the complex plane. Re is the real axis, Im is the imaginary axis, and i is the square root of –1. A complex… …   Wikipedia

• complex number — noun (mathematics) a number of the form a+bi where a and b are real numbers and i is the square root of 1 (Freq. 3) • Syn: ↑complex quantity, ↑imaginary number, ↑imaginary • Topics: ↑mathematics, ↑math, ↑ …   Useful english dictionary

• complex number — kompleksinis skaičius statusas T sritis informatika apibrėžtis Skaičius, išreiškiamas tokia forma: a + bi, kur a ir b yra realieji skaičiai, o i yra šaknis iš 1 ir vadinama menamąja dalimi. Kompleksiniai skaičiai gali būti pavaizduojami taškais… …   Enciklopedinis kompiuterijos žodynas

• complex number — number which is a combination of real and imaginary numbers, non concrete numbers (Mathematics) …   English contemporary dictionary

• complex number — noun Date: 1856 a number of the form a + b √ 1 where a and b are real numbers …   New Collegiate Dictionary

• complex number — noun A number of the form a + bi, where a and b are real numbers and i = minus;1 …   Wiktionary

• complex number — See number …   Philosophy dictionary