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]
(mathematics)
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

(mathematics)
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 ?
If [alpha] is a non-zero complex number such that [Real part] (1/[alpha]) > 0 and if f [member of] A, f(z)/z [not equal to] 0, z [member of] E, satisfies
Students studying a mathematics specialism as a part of the Victorian VCE (Specialist Mathematics, 2010), HSC in NSW (Mathematics Extension in NSW, 1997) or Queensland QCE (Mathematics C, 2009) will be familiar with de Moivre's theorem and its applications to complex numbers (see the short discourse by Bardell (2014) for further details).
For a complex number [micro], if f [member of] A, f'(z) [(z/f(z)).sup.[micro]+1] [not equal to] 0 for all z in E, satisfies the differential subordination
Then, for every real or complex number [alpha] with [absolute value of [alpha]] [greater than or equal to] k,
If f given by (1) is in the class [S.sup.*.sub.q]([phi]) and [mu] is a complex number, then
Definition III: Let A = ([x.sub.0], [x.sub.1], [x.sub.2], ..., [x.sub.n-1]) and B = ([y.sub.0], [y.sub.1], [y.sub.2], ..., [y.sub.n-1]) be two n dimensional complex numbers. Then similarity measure between A and B is defined as, when n is odd
To support data integrity, an integer value b--the difference of the previous sensed value and the current sensed value of the sensor node--with i is appended to the a by using genCpxNum() function to form a complex number C = a + bi, where a and b are real numbers called the real part and the imaginary part of the complex number, respectively, as shown in Table 2.
Suppose [alpha] is a non-zero complex number and a, b are real numbers such that 0 < a < b < 1.
If [f.sup.n]f' - z and [g.sup.n]g' - z share 0 CM, then either [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], where [c.sub.1], [c.sub.2] and c are three nonzero complex numbers satisfying 4[([c.sub.1] [c.sub.2]).sup.n+1][c.sup.2] = -1 or f = tg for a complex number t such that [t.sup.n+1] = 1.
(Step 2) Suppose there exists a complex number z whose absolute value is less than [r.sub.0] and satisfying the condition h(z) = 1.
The Mandelbrot set is just a set of points in this complex number plane.
What pupils choose to eat and drink at school is influenced by a complex number of factors, it said.