complex number

3 definitions found

complex number - 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]

complex number - WordNet (r) 2.1 (2005) :

  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]

complex number - Free On-line Dictionary of Computing (26 May 2007) :

  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)