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...
89 KB (11,602 words) - 11:21, 9 July 2024
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...
27 KB (4,057 words) - 01:57, 2 May 2024
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...
26 KB (3,299 words) - 10:46, 1 June 2024
consist of various extensions or modifications of the complex number system. In modern mathematics, number systems are considered important special examples...
62 KB (7,747 words) - 17:46, 9 July 2024
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...
21 KB (3,325 words) - 22:01, 2 May 2024
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...
32 KB (5,061 words) - 10:03, 13 June 2024
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...
28 KB (4,664 words) - 06:35, 6 July 2024
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,...
31 KB (4,502 words) - 06:57, 17 June 2024
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...
89 KB (13,280 words) - 05:57, 10 July 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