- 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...
-
corresponding point in the
complex plane from the origin. This can be
computed using the
Pythagorean theorem: for any
complex number z=x+iy,{\displaystyle...
- In algebra, a
split complex number (or
hyperbolic number, also
perplex number,
double number) is
based on a
hyperbolic unit j
satisfying j2=1.{\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...
- 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...
-
which 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...
- Γ(z){\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 the integral...
- 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...
-
multiplication by a
complex number of
modulus 1 acts as a rotation. The
complex plane is
sometimes known as the
Argand plane or
Gauss plane. In
complex analysis...