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.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

complex number

any number of the form a + ib, where a and b are real numbers and i = &#221A--1
Collins Discovery Encyclopedia, 1st edition © HarperCollins Publishers 2005

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.
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References in periodicals archive ?
Therefore one could expect to come up with geometrical explanation of quantum interaction, provided we could generalize the metric using imaginary plane:
For an infinitesimal imaginary plane in a flow system, the area stretch of the plane is determined by the following equation (42):
A Hubble image of 1987A (see photo), taken in August and released last week, shows the supernova core surrounded by a ring of glowing gas tilted 47[degrees] from an imaginary plane cutting through the Earth and the stellar core.
Using a set of data points and an algorithm called "least squares(*)," they draw an imaginary plane that would actually lie somewhere under the contact or tangent plane of that part if it were lying on a surface plate.