Source : Webster's Revised Unabridged Dictionary (1913)

Complex \Com"plex\, 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
      ordinary integers.

   Syn: See {Intricate}.

Source : WordNet®

complex number
     n : a number of the form a+bi where a and b are real numbers and
         i is the square root of -1 [syn: {complex quantity}, {imaginary
         number}]

Source : Free On-Line Dictionary of Computing

complex number
     
         A number of the form x+iy where i is the square
        root of -1, and x and y are {real number}s, 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)