1. [syn: complex number, complex quantity, imaginary number, imaginary]
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.
Ideas thus made up of several simple ones put
together, I call complex; such as beauty, gratitude,
a man, an army, the universe. --Locke.
2. Involving many parts; complicated; intricate.
When the actual motions of the heavens are
calculated in the best possible way, the process is
difficult and complex. --Whewell.
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
Syn: See Intricate.
WordNet (r) 3.0 (2006):
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,
The Free On-line Dictionary of Computing (30 December 2018):
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
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.