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complex number

a mathematical expression (a + bi) in which a and b are real numbers and i 2 = −1.
Origin of complex number
1825-35 Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2016.
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British Dictionary definitions for complex number

complex number

any number of the form a + ib, where a and b are real numbers and i = √–1 See number (sense 1)
Collins English Dictionary - Complete & Unabridged 2012 Digital Edition
© William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012
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complex number in Science
complex number
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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complex number in Technology

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.

The Free On-line Dictionary of Computing, © Denis Howe 2010
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