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 ?
As we know, there is linkage between geometry and algebra with imaginary plane [18]:
Spencer and Wiley (40) showed that the area stretch ratio of an imaginary plane depends not only on the strain but also on the direction of the deforming plane, and the area stretch ratio of the flat imaginary plane in simple shear flow is given by
The process is based on looking at the image of the leads and creating a plane from the three worst leads within the center of gravity of the project and measuring the rest of the leads against this imaginary plane, or coplanarity measurement.
David Wang, who also offers an edifying introduction to the anthology, probes the many facets of nostalgia at work in the native-soil fiction of Shen Congwen, Song Zelai, Mo Yan, and Li Yongping, arguing that Li has gone the furthest in relegating the nostalgic setting of The Jiling Chronicles to a pointedly imaginary plane outside the boundaries of a particular region or era.