complex number

(redirected from Complex division)
Also found in: Dictionary, Thesaurus.

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
..... Click the link for more information.

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 hospital with its complex division of labor, the large law firm, the large accounting firm, the multidisciplinary architectural houses--these were all invented in the early years of this century.
Although he insightfully addresses a broad range of theoretical issues of (post)communist studies and comparative politics as a whole, Kopstein frames his study as a critique of the technocratic theory of communist rule, which in the 1960s and 1970s grew out of modernization theory and its prediction of functional convergence in societies with a complex division of labor.
Tenders are invited for Maintenance of staff quarters under Capital Complex Division during the year 2016-17/ SH: Repairing and painting of Type I and Type II quarter at Capital Complex (Type I - 3
Engineer, Sachivalay Electrical Complex Division, "A" Block, 1st Floor, Patnagar Yojana Bhavan, Sector -16, Gandhinagar,
These buildings were built on stone foundations with complex divisions.
The plan would also relax the complex divisions between which offenses are dealt with at federal, state and local levels.
In 1994, Rwanda's government was controlled by the minority Hutu ethnic group, and the complex divisions culminated in the state-orchestrated genocide of an estimated 800,000 Tutsis, the dominant ethnic group.
These controversies continue to influence the complex divisions which lie at the heart of Iraq's Shi'ite politics today.
With scholarship and scrupulous impartiality Lewis explains the complex divisions and rivalries that led to the rise of the assassins and their role in religious politics.
Data for 65 nations, circa 1965, showed that rates of social disorder, measured by Hibbs' internal war index, (1) were highest in countries with low levels of division of labor and high rates of population growth, (2) declined in nations high on population growth but also high on division of labor, (3) dropped even further in countries with complex divisions of labor and slow population growth, but (4) were lowest of all for societies in which both population growth and division of labor were rated as low These data were seen as supporting our interpretation of Durkheim's views.
His chapter on religion is especially interesting and reveals the deep complex divisions of the Lords.