complex number

Webster's Dictionary (GCIDE)

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]

Free On-line Dictionary of Computing

<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)