# complex number

## complex number

noun
a mathematical expression (a + bi ) in which a and b are real numbers and i 2 = −1.

Origin:
1825–35

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Collins
World English Dictionary
 complex number —n See number any number of the form a + ib, where a and b are real numbers and i = √--1

Collins English Dictionary - Complete & Unabridged 10th Edition
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American Heritage
Science Dictionary
 complex number   (kŏm'plěks')  Pronunciation Key  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.
The American Heritage® Science Dictionary
Copyright © 2002. Published by Houghton Mifflin. All rights reserved.
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FOLDOC
Computing Dictionary

### complex number definition

mathematics
A number of the form x+iy where i is the square root of -1, and x and y are real numbers, known as the "real" and "imaginary" part. Complex numbers can be plotted as points on a two-dimensional plane, known as an Argand diagram, where x and y are the Cartesian coordinates.
An alternative, polar notation, expresses a complex number as (r e^it) where e is the base of natural logarithms, and r and t are real numbers, known as the magnitude and phase. The two forms are related:
r e^it = r cos(t) + i r sin(t) = x + i y where x = r cos(t) y = r sin(t)
All solutions of any polynomial equation can be expressed as complex numbers. This is the so-called Fundamental Theorem of Algebra, first proved by Cauchy.
Complex numbers are useful in many fields of physics, such as electromagnetism because they are a useful way of representing a magnitude and phase as a single quantity.
(1995-04-10)
The Free On-line Dictionary of Computing, © Denis Howe 2010 http://foldoc.org
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Example sentences
He asked a moronic question of if complex number exists in physical reality.
Graph showing part of the complex number phase of the gamma function and a related function.
Impedance is a complex number and is described by the magnitude of the ratio and the phase angle between the two measurements.
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