complex number

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complex number:

see numbernumber,
entity describing the magnitude or position of a mathematical object or extensions of these concepts. The Natural Numbers

Cardinal numbers describe the size of a collection of objects; two such collections have the same (cardinal) number of objects if their
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complex number

[′käm‚pleks ′nəm·bər]
Any number of the form a + bi, where a and b are real numbers, and i 2= -1.

complex number

any number of the form a + ib, where a and b are real numbers and i = &#221A--1

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.
References in periodicals archive ?
Let [alpha], fi are complex numbers then we have the following identities
For any positive integer n and complex number s with Re s > 1, we have
Each if statement deals with a special case of displaying the complex number in a standard text field.
While real numbers can be represented as points on a line, complex numbers must be located on a plane.
kappa]](n) is the k-power complement number of any positive number n, and [alpha], [beta] are two complex numbers with Re([alpha]) [greater than or equal to] 1; Re([beta]) [greater than or equal to] 1.
The dual complex numbers defined as the dual quaternions were considered as a generalization of complex numbers by Ata and Yayli [3].
The new formula looks like the original Descartes equation for four mutually tangent circles, provided the coordinates of the centers are expressed as so-called complex numbers.
A Norwegian surveyor, Wessel (1797), and a Parisian book-keeper, Argand (1806), independently suggested that the complex number x + iy can be represented by the point (x, y) in the plane.
It draws a similarity between the two diverse realms: just as ceramic undergoes a complex number of physical changes before being stabilised by fortification, love too is in a state of constant change, from one extreme to another such as 'yes' to 'no', sunny to moody (or at times even stormy), it added.
The missile, which is capable of carrying a conventional warhead of 300 kg, was test-fired from a mobile launcher from launch complex number three of the Integrated Test Range (ITR).
The call handler issued an ambulance to go to her home at Westhope Road, but this was stood down due to the complex number of symptoms so that a clinical nurse from NDUC could assess her over the phone.
New products in the family include the ConnX BBE32EP and BBE64EP, optimized for complex number processing at low power and ideally suited for smartphones and tablets, HDTVs, set-top boxes, and automotive communications infrastructure system applications.