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 ?
The same effect also occurs when a complex number is multiplied by i.
n]g' - P share 0 CM, then either f = tg for a complex number t satisfying [t.
Any complex number t on the circle {t [member of] C | [absolute value of t] = r} satisfies
In the course of algebra, two algorithms are used to solve algebraic equations of any degree, the first one--on the set of the generally understood real numbers, the second one--on the set of the generally incomprehensible complex numbers.
where [sigma] is an arbitrary complex number, s an integer [greater than or equal to] 1.
Analyzing and evaluating the effectiveness of some implemented models of ICT tools in teaching mathematics, regarding the teaching of complex numbers and interactive geometry, are problems of this paper.
the authentication process is carved out by the calculation or the auxiliary arguments; the first and the second are continuous functions, and the third is a complex number.
The Fundamental Theorem of Algebra (FTAL) states that if f(x) is a polynomial of degree n, where n is a positive integer, then f has at least one zero in the Complex numbers system, and f(x) can be written of n linear factor with coefficients in Complex numbers system.
When each complex number is decomposed into two real components, there are 16 X [10.
Yet even he recognises the limitations of a single book trying to cover such a complex number of subjects.
We look forward to continuing to manage this complex number system that so many telecommunications service providers and their consumers rely on.
The focus in these examples is on the extent to which students display an awareness of structure in complex number and algebraic expressions.