• Thumbnail for 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...
    91 KB (12,021 words) - 17:33, 29 May 2025
  • Thumbnail for 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...
    27 KB (3,477 words) - 09:59, 20 April 2025
  • 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...
    28 KB (4,144 words) - 21:21, 22 March 2025
  • Thumbnail for 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...
    14 KB (1,951 words) - 10:08, 20 April 2025
  • Thumbnail for 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...
    22 KB (3,390 words) - 14:25, 10 June 2025
  • Thumbnail for 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...
    30 KB (4,831 words) - 06:58, 24 March 2025
  • Thumbnail for Number
    consist of various extensions or modifications of the complex number system. In modern mathematics, number systems are considered important special examples...
    66 KB (8,359 words) - 15:41, 10 June 2025
  • Thumbnail for Algebraic number
    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 +...
    17 KB (2,298 words) - 15:08, 5 June 2025
  • Thumbnail for 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,...
    31 KB (4,502 words) - 23:12, 6 May 2025
  • Thumbnail for Circle group
    {\displaystyle \mathbb {T} } is as well. A unit complex number in the circle group represents a rotation of the complex plane about the origin and can be parametrized...
    13 KB (2,078 words) - 16:41, 10 January 2025
  • (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...
    12 KB (1,347 words) - 02:23, 8 May 2025
  • Thumbnail for Gamma function
    {\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...
    90 KB (13,517 words) - 14:18, 9 June 2025
  • Thumbnail for Exponentiation
    base b {\displaystyle b} and any real number exponent x {\displaystyle x} . More involved definitions allow complex base and exponent, as well as certain...
    104 KB (13,637 words) - 11:23, 4 June 2025
  • Thumbnail for 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...
    12 KB (1,856 words) - 13:56, 3 May 2025
  • Thumbnail for 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...
    33 KB (5,220 words) - 16:24, 25 May 2025
  • Thumbnail for Complex analysis
    investigates functions of complex numbers. It is helpful in many branches of mathematics, including algebraic geometry, number theory, analytic combinatorics...
    18 KB (2,538 words) - 09:09, 12 May 2025
  • Thumbnail for Euler's formula
    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...
    27 KB (3,950 words) - 21:03, 8 June 2025
  • complex, a coordination complex with more than one bond Complex number, an extension of real numbers obtained by adjoining imaginary numbers Complex,...
    3 KB (428 words) - 07:55, 29 December 2024
  • Thumbnail for Constructible number
    {\displaystyle q} as a complex number. In the other direction, any formula for an algebraically constructible complex number can be transformed into...
    33 KB (4,921 words) - 20:46, 11 June 2025
  • In mathematics, a Gaussian rational number is a complex number of the form p + qi, where p and q are both rational numbers. The set of all Gaussian rationals...
    3 KB (404 words) - 20:22, 31 October 2024
  • In mathematics, a transcendental number is a real or complex number that is not algebraic: that is, not the root of a non-zero polynomial with integer...
    52 KB (6,816 words) - 13:34, 18 May 2025
  • Thumbnail for Sign (mathematics)
    described in § Other meanings below. Numbers from various number systems, like integers, rationals, complex numbers, quaternions, octonions, ... may have multiple...
    29 KB (2,740 words) - 09:55, 12 April 2025
  • Thumbnail for Gaussian integer
    In number theory, a Gaussian integer is a complex number whose real and imaginary parts are both integers. The Gaussian integers, with ordinary addition...
    35 KB (4,835 words) - 07:01, 5 May 2025
  • Thumbnail for Cube root
    integer or of a rational number is generally not a rational number, neither a constructible number. Every nonzero real or complex number has exactly three cube...
    15 KB (2,266 words) - 16:35, 21 May 2025
  • Thumbnail for Periodic function
    periodic; in the case of Dirichlet function, any nonzero rational number is a period. Using complex variables we have the common period function: e i k x = cos...
    12 KB (1,704 words) - 00:48, 17 March 2025
  • Thumbnail for Phasor
    Phasor (redirect from Complex amplitude)
    physics and engineering, a phasor (a portmanteau of phase vector) is a complex number representing a sinusoidal function whose amplitude A and initial phase...
    31 KB (4,997 words) - 08:14, 17 January 2025
  • in the complex numbers. That is, for any non-constant polynomial P {\displaystyle P} with rational coefficients there will be a complex number α {\displaystyle...
    29 KB (3,907 words) - 01:54, 18 February 2025
  • in late 1938 with Stibitz at the helm. He led the development of the Complex Number Calculator (CNC), completed in November 1939 and put into operation...
    17 KB (1,849 words) - 09:28, 25 May 2025
  • Thumbnail for Square root
    called the complex numbers, that does contain solutions to the square root of a negative number. This is done by introducing a new number, denoted by...
    48 KB (6,213 words) - 21:46, 11 June 2025
  • Thumbnail for Polar coordinate system
    }}y<0\\{\text{undefined}}&{\mbox{if }}r=0.\end{cases}}} Every complex number can be represented as a point in the complex plane, and can therefore be expressed by specifying...
    49 KB (6,702 words) - 21:47, 13 May 2025