Search Result for "complex number":
Wordnet 3.0

NOUN (1)

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]


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]
WordNet (r) 3.0 (2006):

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]
The Free On-line Dictionary of Computing (30 December 2018):

complex number 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)