complex number wikipedia - EAS
- From Wikipedia, the free encyclopedia. A complex number is a number, but is different from common numbers in many ways. A complex number is made up using two numbers combined together. The first part is a real number, and the second part is an imaginary number. The most important imaginary number is called.
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Alles weergeven op Wikipediahttps://en.wikipedia.org/wiki/Complex_numberIn mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted i, called the imaginary unit and satisfying the equation i = −1; every complex number can be expressed in the form a + bi, where a and b are real numbers. Because no real … Meer weergeven
A complex number is a number of the form a + bi, where a and b are real numbers, and i is an indeterminate satisfying i = −1. For example, 2 + 3i is a complex number.
This way, a complex number is defined as a Meer weergevenThe solution in radicals (without trigonometric functions) of a general cubic equation, when all three of its roots are real … Meer weergeven
Field structure
The set of complex numbers is a field. Briefly, this means that the following facts hold: first, any two complex numbers can be added … Meer weergevenA real number a can be regarded as a complex number a + 0i, whose imaginary part is 0. A purely imaginary number bi is a complex number 0 + bi, whose real part is zero. As with … Meer weergeven
A complex number z can thus be identified with an ordered pair of real numbers, which in turn may be interpreted as coordinates of a point in … Meer weergeven
Equality
Complex numbers have a similar definition of equality to real numbers; two complex numbers a1 … Meer weergevenConstruction as ordered pairs
William Rowan Hamilton introduced the approach to define the set of complex numbers as the set of ordered pairs (a, b) of real numbers, in which the following rules for addition and multiplication are imposed:
It is then just … Meer weergevenWikipedia-tekst onder CC-BY-SA-licensie- https://nl.wikipedia.org/wiki/Complex_getal
In de wiskunde zijn complexe getallen een uitbreiding van de reële getallen. Zoals de reële getallen overeenkomen met punten op een rechte lijn, correspondeert elk complex getal met een punt uit een vlak. Een complex getal is zodoende een paar reële getallen en , dat gewoonlijk weergegeven wordt als . Hierin is (soms wordt ook gebruikt) een bijzonder complex getal, de imaginaire eenheid, met als eigenschap . Met complexe getallen in de vorm kan gewoon gereken…
Wikipedia · Tekst onder CC-BY-SA-licentie- Geschatte leestijd: 8 min.
- https://simple.wikipedia.org/wiki/Complex_number
A complex number is made up using two numbers combined. The first part is a real number , and the second part is an imaginary number . The most important imaginary number is called …
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- https://en.wikipedia.org/wiki/Split-complex_number
- In algebra, a split complex number has two real number components x and y, and is written z = x + y j, where j2 = 1. The conjugate of z is z∗ = x − y j. Since j2 = 1, the product of a number z with its conjugate is zz∗ = x2 − y2, an isotropic quadratic form, =N = x2 − y2. The collection D of all split complex numbers z = x + y j for x, y ∈ R forms ...
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- https://en.wikipedia.org/wiki/Argument_(complex_analysis)
- In mathematics, the argument of a complex number z, denoted arg, is the angle between the positive real axis and the line joining the origin and z, represented as a point in the complex plane, shown as φ {\displaystyle \varphi } in Figure 1. It is a multi-valued function operating on the nonzero complex numbers. To define a single-valued function, ...
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- https://en.wikipedia.org/wiki/Complex_conjugate
In mathematics, the complex conjugate of a complex number is the number with an equal real part and an imaginary part equal in magnitude but opposite in sign. That is, the complex conjugate of a + b i {\displaystyle a+bi} is equal to a …
- https://en.wikipedia.org/wiki/Number
The first known documented use of zero dates to AD 628, and appeared in the Brāhmasphuṭasiddhānta, the main work of the Indian mathematician Brahmagupta.He treated …
- https://en.wikipedia.org/wiki/Bicomplex_number
Bicomplex numbers form an algebra over C of dimension two, and since C is of dimension two over R, the bicomplex numbers are an algebra over R of dimension four. In fact the real …
- https://en.wikipedia.org/wiki/Imaginary_number
Geometrically, imaginary numbers are found on the vertical axis of the complex number plane, which allows them to be presented perpendicular to the real axis. One way of viewing …
- https://en.wikipedia.org/wiki/Complex
Complex number, an extension of real numbers obtained by adjoining imaginary numbers; Complex polytope, a generalization of a polytope in a complex Hilbert space; Complex …
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