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...

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...

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...

consist of various extensions or modifications of the complex number system. In modern mathematics, number systems are considered important special examples...

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...

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...

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...

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,...

{\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...

investigates functions of complex numbers. It is helpful in many branches of mathematics, including algebraic geometry, number theory, analytic combinatorics...