# Category: Complex numbers

Complex conjugate
In mathematics, the complex conjugate of a complex number is the number with an equal real part and an imaginary part equal in magnitude but opposite in sign. That is, (if and are real, then) the comp
Root of unity
In mathematics, a root of unity, occasionally called a de Moivre number, is any complex number that yields 1 when raised to some positive integer power n. Roots of unity are used in many branches of m
Complex plane
In mathematics, the complex plane is the plane formed by the complex numbers, with a Cartesian coordinate system such that the x-axis, called the real axis, is formed by the real numbers, and the y-ax
Principal root of unity
In mathematics, a principal n-th root of unity (where n is a positive integer) of a ring is an element satisfying the equations In an integral domain, every primitive n-th root of unity is also a prin
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 unit and satisfying the equation ; every complex
Jean-Robert Argand
Jean-Robert Argand (UK: /ˈɑːrɡænd/, US: /ˌɑːrˈɡɑːn(d)/, French: [ʒɑ̃ ʁɔbɛʁ aʁɡɑ̃]; July 18, 1768 – August 13, 1822) was an amateur mathematician. In 1806, while managing a bookstore in Paris, he publi
Imaginary number
An imaginary number is a real number multiplied by the imaginary unit i, which is defined by its property i2 = −1. The square of an imaginary number bi is −b2. For example, 5i is an imaginary number,
Mean value problem
In mathematics, the mean value problem was posed by Stephen Smale in 1981. This problem is still open in full generality. The problem asks: For a given complex polynomial of degree and a complex numbe
Imaginary unit
The imaginary unit or unit imaginary number (i) is a solution to the quadratic equation . Although there is no real number with this property, i can be used to extend the real numbers to what are call
Caspar Wessel
Caspar Wessel (8 June 1745, Vestby – 25 March 1818, Copenhagen) was a Danish–Norwegian mathematician and cartographer. In 1799, Wessel was the first person to describe the geometrical interpretation o
Table of Gaussian integer factorizations
A Gaussian integer is either the zero, one of the four units (±1, ±i), a Gaussian prime or composite. The article is a table of Gaussian Integers x + iy followed either by an explicit factorization or
External ray
An external ray is a curve that runs from infinity toward a Julia or Mandelbrot set.Although this curve is only rarely a half-line (ray) it is called a ray because it is an image of a ray. External ra
Quater-imaginary base
The quater-imaginary numeral system was first proposed by Donald Knuth in 1960. It is a non-standard positional numeral system which uses the imaginary number 2i as its base. It is able to uniquely re
Complex conjugate line
In complex geometry, the complex conjugate line of a straight line is the line that it becomes by taking the complex conjugate of each point on this line. This is the same as taking the complex conjug
Complex-base system
In arithmetic, a complex-base system is a positional numeral system whose radix is an imaginary (proposed by Donald Knuth in 1955) or complex number (proposed by S. Khmelnik in 1964 and in 1965).