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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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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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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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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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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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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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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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...
90 KB (13,350 words) - 00:29, 3 August 2024
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...
26 KB (3,832 words) - 03:31, 6 August 2024
investigates functions of complex numbers. It is helpful in many branches of mathematics, including algebraic geometry, number theory, analytic combinatorics...
18 KB (2,517 words) - 14:08, 22 April 2024