complex number

noun

a mathematical expression (a + bi) in which a and b are real numbers and i ² = −1.

Origin

1825-35

Examples from the web for complex number

He asked a moronic question of if complex number exists in physical reality.
Graph showing part of the complex number phase of the gamma function and a related function.
Impedance is a complex number and is described by the magnitude of the ratio and the phase angle between the two measurements.

British Dictionary definitions for complex number

complex number

noun

any number of the form a + ib, where a and b are real numbers and i = √–1 See number (sense 1)

complex number in Science

complex number

(kŏm'plěks')
A number that can be expressed in terms of i (the square root of -1). Mathematically, such a number can be written a + bi, where a and b are real numbers. An example is 4 + 5i.

complex number in Technology

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)