complex number

Definitions

  • WordNet 3.6
    • n complex number (mathematics) a number of the form a+bi where a and b are real numbers and i is the square root of -1
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Webster's Revised Unabridged Dictionary
    • Complex number (Math) in the theory of numbers, an expression of the form a + b√-1, when a and b are ordinary integers.
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Quotations

  • Albert Einstein
    Albert%20Einstein
    “When the number of factors coming into play in a phenomenological complex is too large scientific method in most cases fails.”

Usage

In literature:

As the communities along the Nile grew in size and number, society began to develop a complex urban civilization.
"The Black Experience in America" by Norman Coombs
He was also charged with a theft-of-service misdemeanor, involving a complex free-call scam to a 900 number.
"Hacker Crackdown" by Bruce Sterling
As social life grows more complex, these factors increase in number and import.
"Democracy and Education" by John Dewey
A vast number of complex movements are reflex.
"The Expression of Emotion in Man and Animals" by Charles Darwin
But the peace was to be short-lived, because it was threatened by the emergence of a number of other problems of great complexity.
"The Expansion of Europe" by Ramsay Muir
He was watching Number One's bungalow with an animal-like patience, if with a very human complexity of purpose.
"Victory" by Joseph Conrad
We can neither regulate the complexity of our environment nor the number of problems which we must settle within a given time.
"Industrial Progress and Human Economics" by James Hartness
In 1685, he introduced the first graphical representation of complex numbers.
"Our Legal Heritage, 5th Ed." by S. A. Reilly
Difference in number does not indicate difference in complexity.
"Harvard Psychological Studies, Volume 1" by Various
Like imitation, therefore, play seems a complex, involving a number of instinctive tendencies.
"Ontario Normal School Manuals: Science of Education" by Ontario Ministry of Education
But let us say at once that a number of other cases render the problem much more complex.
"Mrs. Piper & the Society for Psychical Research" by Michael Sage
It becomes established as life grows more complex, as specific desires increase in number.
"The Psychology of Nations" by G.E. Partridge
Thirdly, it must be a rather complex situation in order that the judgment may be influenced by a number of motives.
"Psychology and Social Sanity" by Hugo Münsterberg
A large number of them have inscriptions in a complex cuneiform character peculiar to Babylon.
"Museum of Antiquity" by L. W. Yaggy
Polytheism is a complex product; it is the addition to each other of a number of cults which have grown up separately.
"History of Religion" by Allan Menzies
He cannot put together in his mind a great number of sounds, nor interpret complex ideas in detail.
"The Speech of Monkeys" by R. L. Garner
All vessels of the coracoid complex are exceedingly variable, in number, size, and site of origin.
"Thoracic and Coracoid Arteries In Two Families of Birds, Columbidae and Hirundinidae" by Marion Anne Jenkinson
Its identity puzzled biologists for years, and they had a number of complex theories to explain it away.
"Sense of Obligation" by Henry Maxwell Dempsey (AKA Harry Harrison)
While they consist of a "dual" thread, each unit of these is complex, being made up of a number of fibrillae.
"Encyclopaedia Britannica, 11th Edition, Volume 10, Slice 3" by Various
A great number of complex receipts are in use among manufacturers of these articles.
"Popular Technology; Volume 2" by Edward Hazen
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In news:

Local law enforcement is attempting to create a database of all the phone numbers for local households in the county so residents can be notified of emergencies and disasters in their area, such as the Inyo Complex Flood of 2008.
Complexity doesn't come from the number of brackets.
But it does, with complex spicing and vibrant flavours that raise a number of the dishes above the ordinary.
A number of the new tenants of Morgan Woods, Edgartown's affordable rental housing complex, were short on home furnishings.
With that, I knew x^2 - 2 x + 17 had a solution in complex numbers.
I didn't come across complex numbers again until I saw the Mandelbrot set for the first time.
The complexity of the physically driven locomotion used in skate means that, at any given point, there is an extremely large number of degrees of freedom in potential motion.
There is a chronic shortage of man power, money and system bandwidth to deal with the ever increasing number and complexity of IT security threats.
Created by celebrity trainer and fitness guru Harley Pasternak , the "five" in the 5 Factor Diet comes from the number of elements each meal should include – protein, complex carbs, fiber, fat and fluids.
Volume 85, Number 32 p. CONTROLLING THE FORMATION of complex polymeric nanostructures is no easy task.
With thousand-dollar bottles, complex classifications and a dizzying number of estates, this great French wine region is difficult to comprehend.
Creating business value is a multifacted process that requires a number of areas of problem solving–of dealing with complexity in various forms.
Some Treasure Coast apartment complexes converted into condominiums during the housing boom are now cash-strapped communities grappling with a crippling number of foreclosures and unpaid maintenance dues.
The Baltimore Orioles have managed to negotiate their way out of new spring training homes a number of times over the past 15 years, including the fabulous Disney complex that the Atlanta Braves call their spring training home.
It has claimed responsibility for a number of complex attacks in Damascus and Aleppo, frequently involving suicide bombers.
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In science:

The above result generalizes to the case when instead of the hypothesis “R ρij = q” we start with “R ρij = z ”, where z is a complex number such that |z | < 1.
Random unitaries in non-commutative tori, and an asymptotic model for q-circular systems
Let (A, ϕ) be a C ∗ -probability space, and let z be a complex number such that |z | < 1.
Random unitaries in non-commutative tori, and an asymptotic model for q-circular systems
So, let us fix a complex number z such that |z | < 1.
Random unitaries in non-commutative tori, and an asymptotic model for q-circular systems
VlVm = γlmVmVl , 1 ≤ l < m ≤ p, where the γlm ’s are some complex numbers.
Random unitaries in non-commutative tori, and an asymptotic model for q-circular systems
The eigenvalues of such a matrix are unit quaternions and therefore doubly degenerate in the representation of the Dirac matrix as complex numbers.
Random Matrix Theory and Chiral Symmetry in QCD
These magic numbers are directly related to the existence of the four fundamental algebraic structures: real numbers, complex numbers, quaternions and octonions.
Dyon-Oscillator Duality
For the unitary group U (n, C ) over the complex numbers, two matrices are in the same conjugacy class if and only if they have the same set of eigenvalues.
Random matrix theory over finite fields: a survey
For β = 2 the matrix elements of the Dirac operator do not have any reality properties and are given by complex numbers.
Spectral Universality of Real Chiral Random Matrix Ensembles
Therefore the map z → ζ transforms the quadrant {Imz > 0, Rez > 0} into the to the upper semi-plane {Reζ > 0}, cut along an arc connecting the points c and b, where b is some complex number (Fig. 1).
Exact Solution of the Three-color Problem on a Random Lattice
Suppose that V is a finite-dimensional vector space over the complex numbers.
Random walks on wreath products of groups
Let q be a complex number such that 0 < |q | < 1.
A simple proof of Bailey's very-well-poised 6-psi-6 summation
This is related to the fact that these generators involve a complex numbers q1,2 and p which are different from ±1.
Fractional Supersymmetry through Generalized Anyonic algebra
We work over C, the field of complex numbers.
The Hodge Conjecture for general Prym varieties
Since α/β can be an arbitrary complex number, R2 W can take any real value if C 6= 0, including zero and negative values.
Defining Entropy Bounds
In the scalar case, that is, when F = G = C is the space of complex numbers in the Euclidean metric, we write simply Sκ .
A note on interpolation in the generalized Schur class
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