complex number

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Related to Imaginary plane: imaginary part, Imaginary axis, Argand plane

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 ?
Our proposition is that considering equation (30) has imaginary plane wave, therefore it could be expected to provided "physical mechanism" of quantum interaction, in the same sense of equation (14).
For an infinitesimal imaginary plane in a flow system, the area stretch of the plane is determined by the following equation (42):
where [eta] is the area stretch ratio of the infinitesimal imaginary plane, \[dA.
In practice, it involves shining a laser beam into the eye and focusing it on an imaginary plane near the top of the optic nerve head.
Army jawans used state of the art technology and modern weapons and targeted the enemys imaginary planes successfully which had intruded into Pakistan air space.