- 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 + i y , {\displaystyle...
- 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...
-
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...
- for
which the
polynomial evaluates to zero. As
another example, the
complex number 1 + i {\displaystyle 1+i} is
algebraic because it is a root of x4 +...
-
consist of
various extensions or
modifications of the
complex number system. In
modern mathematics,
number systems are
considered important special examples...
- 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,...
- (in the
early 19th century). An
imaginary number bi can be
added to a real
number a to form a
complex number of the form a + bi,
where the real numbers...
