Complex number
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Complex number
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...
Absolute value
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...
Split-complex number
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...
Argument (complex analysis)
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...
Complex logarithm
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...
Riemann sphere
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...
Number
preceding one. So, for example, a rational number is also a real number, and every real number is also a complex number. This chain of set inclusions can be...
Gamma function
{\displaystyle \Gamma (z)} is due to Legendre. If the real part of the complex number z {\displaystyle z} is strictly positive ( ℜ ( z ) > 0 {\displaystyle...
Complex plane
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,...
Electrical 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...