from
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]
from
The Free On-line Dictionary of Computing (8 July 2008)
complex number
<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)