Search Result for "complex number":
Wordnet 3.0

NOUN (1)

1. (mathematics) a number of the form a+bi where a and b are real numbers and i is the square root of -1;
[syn: complex number, complex quantity, imaginary number, imaginary]

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The Collaborative International Dictionary of English v.0.48: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; a complex idea.
[1913 Webster]

Ideas thus made up of several simple ones put
together, I call complex; such as beauty, gratitude,
a man, an army, the universe.         --Locke.
[1913 Webster]

2. Involving many parts; complicated; intricate.
[1913 Webster]

When the actual motions of the heavens are
calculated in the best possible way, the process is
difficult and complex.                --Whewell.
[1913 Webster]

Complex fraction. See Fraction.

Complex number (Math.), in the theory of numbers, an
expression of the form a + b[root]-1, when a and b are
ordinary integers.

Syn: See Intricate.
[1913 Webster]

WordNet (r) 3.0 (2006):complex number
n 1: (mathematics) a number of the form a+bi where a and b are
real numbers and i is the square root of -1 [syn: complex
number, complex quantity, imaginary number,
imaginary]

The Free On-line Dictionary of Computing (30 December 2018):complex number

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)
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