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 ?
Because these chapters were delivered as lectures, there are some repetitions that would be necessary if these complex arguments were only heard and not read; for the book, these could have been edited down with little or no loss to our appreciation of Dempsey's layered argument and evidence.
It's a complex argument and one that will continue to rage about everything from fruit pickers to the people who rear and milk our cows.
As a general rule, having a complex argument is not good.
Gray attempts to make a very complex argument regarding the definition of strategic culture, but much of the chapter is focused on a debate with Iain Johnston, which readers unfamiliar with this literature may find particularly daunting.
Hauser's description of the cultural pattern in our southern states, coming from a Harvard professor, could become a little controversial if it weren't buried rather deeply in his otherwise complex argument.
Fornari: It is an articulated and complex argument because, to reconstruct it, we must unite explicit observations of Leonardo with what can be deduced from other testimonies, above all from his own works.
He said: "It's a complex argument which we haven't won with the Government yet.
John Sidel develops a complex argument for global and local-national factors in jihadist movements in the Philippines and Indonesia.
In taking on this project, Harris quotes amply from existing Burroughs scholarship and puts forth a complex argument that presupposes a knowledge of such seminal critical theorists as Walter Benjamin, Jacques Lacan, Maurice Blanchot, and Guy Debord, among others.
This style is a strength because it allows the framework of his complex argument to stay in the foreground.
Although my account has simplified a rich and complex argument, one can begin to see how the roots of the accommodation vs.
He notes that the acceleration of media consumption and reduced audience attentiveness to any one text may threaten complex argument and storytelling, but can also replace reverence for the media with healthy skepticism.

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