In 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...
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Absolute value (redirect from Modulus of complex number)
corresponding point in the complex plane from the origin. This can be computed using the Pythagorean theorem: for any complex number z = x + i y , {\displaystyle...
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In algebra, a split-complex number (or hyperbolic number, also perplex number, double number) is based on a hyperbolic unit j satisfying j 2 = 1. {\displaystyle...
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Riemann sphere (redirect from Extended complex number)
Bernhard Riemann, is a model of the extended complex plane (also called the closed complex plane): the complex plane plus one point at infinity. This extended...
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consist of various extensions or modifications of the complex number system. In modern mathematics, number systems are considered important special examples...
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multiplication by a complex number of modulus 1 acts as a rotation. The complex plane is sometimes called the Argand plane or Gauss plane. In complex analysis,...
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are strongly related: A complex logarithm of a nonzero complex number z {\displaystyle z} , defined to be any complex number w {\displaystyle w} for which...
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Euler's formula (redirect from Eulers formula in complex analysis)
respectively. This complex exponential function is sometimes denoted cis x ("cosine plus i sine"). The formula is still valid if x is a complex number, and is also...
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investigates functions of complex numbers. It is helpful in many branches of mathematics, including algebraic geometry, number theory, analytic combinatorics...
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Gamma function (redirect from Complex number factorial)
{\displaystyle \Gamma (z)} is due to Legendre. If the real part of the complex number z is strictly positive ( ℜ ( z ) > 0 {\displaystyle \Re (z)>0} ), then...
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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...
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In mathematics (particularly in complex analysis), the argument of a complex number z, denoted arg(z), is the angle between the positive real axis and...
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(in the early 19th century). An imaginary number bi can be added to a real number a to form a complex number of the form a + bi, where the real numbers...
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In mathematics, a transcendental number is a real or complex number that is not algebraic – that is, not the root of a non-zero polynomial with integer...
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Electrical impedance (redirect from Complex electric impedance)
resistance, which has only magnitude. Impedance can be represented as a complex number, with the same units as resistance, for which the SI unit is the ohm...
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Sign (mathematics) (redirect from Nonnegative number)
described in § Other meanings below. Numbers from various number systems, like integers, rationals, complex numbers, quaternions, octonions, ... may have multiple...
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Circle group (redirect from Unit complex number)
{\displaystyle \mathbb {T} } is as well. A unit complex number in the circle group represents a rotation of the complex plane about the origin and can be parametrized...
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uncountable complex numbers. In that sense, almost all complex numbers are transcendental. All rational numbers are algebraic. Any rational number, expressed...
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Imaginary unit (redirect from Complex Unit)
numbers to what are called complex numbers, using addition and multiplication. A simple example of the use of i in a complex number is 2 + 3i. Imaginary numbers...
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Inequality (mathematics) (redirect from Complex number inequality)
mathematical expressions. It is used most often to compare two numbers on the number line by their size. The main types of inequality are less than and greater...
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Exponentiation (redirect from Complex numbers exponential)
discussion of powers of the complex number i, see § nth roots of a complex number. The limit of a sequence of powers of a number greater than one diverges;...
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Phasor (redirect from Complex amplitude)
physics and engineering, a phasor (a portmanteau of phase vector) is a complex number representing a sinusoidal function whose amplitude (A), and initial...
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1938 with Stibitz at the helm. Their Complex Number Computer, completed 8 January 1940, was able to calculate complex numbers. In a demonstration to the...
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complex, a coordination complex with more than one bond Complex number, an extension of real numbers obtained by adjoining imaginary numbers Complex polytope...
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programming languages provide a complex data type for complex number storage and arithmetic as a built-in (primitive) data type. A complex variable or value is usually...
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Square root (redirect from Complex square root)
called the complex numbers, that does contain solutions to the square root of a negative number. This is done by introducing a new number, denoted by...
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Complex modulus may refer to: Modulus of complex number, in mathematics, the norm or absolute value, of a complex number: | x + i y | = x 2 + y 2 {\displaystyle...
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Gaussian integer (redirect from Complex integers)
In number theory, a Gaussian integer is a complex number whose real and imaginary parts are both integers. The Gaussian integers, with ordinary addition...
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number. Winding numbers play a very important role throughout complex analysis (c.f. the statement of the residue theorem). In the context of complex...
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Polar coordinate system (redirect from Polar form of a complex number)
}}y<0\\{\text{undefined}}&{\mbox{if }}r=0.\end{cases}}} Every complex number can be represented as a point in the complex plane, and can therefore be expressed by specifying...
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