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• Complex number
  ...unter complex numbers when solving [[quadratic equation]]s, which can have complex number solutions. This presentation is historically misleading — the quadratic ...squares are negative. A historical example of this can be found on the [[Complex number/Advanced|"advanced" subpage]] for this article.
  18 KB (3,028 words) - 17:12, 25 August 2013
• Complex Number
  #REDIRECT [[Complex number]]
  28 bytes (3 words) - 15:30, 28 October 2007
• Complex number/Essentials
  58 bytes (5 words) - 11:05, 13 August 2007
• Complex number/Bibliography
  899 bytes (119 words) - 17:42, 26 September 2007
• Complex number/Approval
  Created [[Complex number/Draft]] [[User:David Tribe|David Tribe]] 19:30, 6 May 2007 (CDT)
  2 KB (190 words) - 10:10, 26 December 2009
• Complex number/Advanced
  ...r by [[William Rowan Hamilton]] in 1837; this construction is explained [[Complex number#Formal definition|later in this article]].
  4 KB (685 words) - 00:41, 6 May 2008
• Complex number/Definition
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• Complex number/Related Articles
  276 bytes (34 words) - 10:41, 21 April 2010
• Complex number/Citable Version
  ...r by [[William Rowan Hamilton]] in 1837; this construction is explained [[Complex number#Formal definition|later in this article]]. ...i</math>. In this way, the real number <math>a</math> is considered as the complex number <math>a + 0i</math> whose imaginary part is zero.
  20 KB (3,304 words) - 17:11, 25 August 2013

Page text matches

• Riemann zeta function/Definition
  [[function (mathematics)|Mathematical function]] of a [[complex number|complex]] variable important in [[number theory]] for its connection with t
  219 bytes (27 words) - 16:59, 13 November 2008
• Imaginary number/Definition
  ...square is a negative real number, or (sometimes) more generally a non-real complex number.
  170 bytes (23 words) - 09:38, 1 January 2010
• Several complex variables/Definition
  ...which characterize [[Function (mathematics)|functions]] of more than one [[Complex number|complex variable]].
  232 bytes (27 words) - 04:54, 22 February 2011
• Real part
  #REDIRECT [[Complex number#Working with complex numbers]]
  57 bytes (7 words) - 13:38, 20 November 2008
• Imaginary part
  #REDIRECT [[Complex number#Working with complex numbers]]
  57 bytes (7 words) - 14:05, 20 November 2008
• Fundamental Theorem of Algebra/Definition
  ...onstant polynomial whose coefficients are complex numbers has at least one complex number as a root.
  144 bytes (20 words) - 02:59, 15 November 2008
• Complex conjugation
  In [[mathematics]], '''complex conjugation''' is an operation on [[complex number]]s which reverses the sign of the imaginary part, that is, it sends <math>z In the [[Complex number#Geometric interpretation|geometrical interpretation]] in terms of the [[Arg
  906 bytes (139 words) - 13:16, 20 November 2008
• Complex analysis/Definition
  ...se properties which characterize [[Function (mathematics)|functions]] of [[Complex number|complex variables]].
  220 bytes (24 words) - 04:46, 22 February 2011
• Number/Related Articles
  {{r|Complex number}}
  258 bytes (33 words) - 02:29, 8 February 2009
• Real number/Related Articles
  *[[Complex number]]
  389 bytes (39 words) - 12:37, 4 January 2009
• Complex numbers
  #REDIRECT [[complex number]]
  28 bytes (3 words) - 16:26, 22 April 2007
• Imaginary unit
  #REDIRECT[[complex number]]
  27 bytes (3 words) - 18:02, 26 April 2007
• Complex Number
  #REDIRECT [[Complex number]]
  28 bytes (3 words) - 15:30, 28 October 2007
• Imaginary number
  The '''imaginary numbers''' are a part of the [[complex number]]s. Every complex number can be written as
  3 KB (468 words) - 17:28, 1 January 2010
• Natural number/Related Articles
  {{r|Complex number}}
  291 bytes (36 words) - 08:06, 19 August 2009
• Complex analysis/Related Articles
  {{r|Complex number}}
  670 bytes (80 words) - 08:52, 7 August 2008
• Algebraic number/Advanced
  ...Historically, such a field was often considered to be a subfield of the [[complex number]]s, but several recent authors have dropped this requirement. An algebraic
  1 KB (179 words) - 14:14, 10 December 2008
• Scalar/Definition
  Real or complex number, or an invariant under orthogonal/unitary transformation of reference fram
  136 bytes (17 words) - 11:40, 25 November 2009
• Modulus (disambiguation)
  {{r|Modulus of a complex number}}
  205 bytes (29 words) - 15:13, 10 January 2024
• Algebraic number/Definition
  A complex number that is a root of a polynomial with rational coefficients.
  111 bytes (16 words) - 16:34, 13 July 2008
• Residue (mathematics)/Definition
  Complex number which describes the behavior of line integrals of a meromorphic function ar
  146 bytes (19 words) - 11:27, 4 September 2009
• Imaginary number/Related Articles
  {{r|Complex number}}
  183 bytes (22 words) - 17:31, 1 January 2010
• Removable singularity
  ...a type of [[singularity]] of a [[function (mathematics)|function]] of a [[complex number|complex]] variable which may be removed by redefining the function value at
  929 bytes (138 words) - 02:29, 25 October 2013
• Isolated singularity
  In [[complex analysis]], an '''isolated singularity''' of a [[complex number|complex]]-valued [[function (mathematics)|function]] is a point at which th
  903 bytes (137 words) - 16:34, 11 November 2008
• Field (mathematics)/Related Articles
  {{r|Complex number}}
  1 KB (146 words) - 16:32, 11 January 2010
• Transcendental number
  In [[mathematics]], a '''transcendental number''' is any [[complex number]] that is not [[algebraic number|algebraic]], i.e. it is not a root of any
  875 bytes (130 words) - 12:27, 8 May 2008
• Arithmetic function
  ...[[positive integer]]s, usually with [[integer]], [[real number|real]] or [[complex number|complex]] values.
  1 KB (159 words) - 06:03, 15 June 2009
• Algebraic number/Related Articles
  {{r|Complex number}}
  887 bytes (126 words) - 02:29, 22 December 2008
• Field extension/Related Articles
  {{r|Complex number}}
  857 bytes (112 words) - 16:32, 11 January 2010
• Domain (disambiguation)
  ...s]], a domain is an [[open set]], usually in the [[real number|real]] or [[complex number]]s
  486 bytes (71 words) - 12:37, 31 May 2009
• Irrational number/Related Articles
  {{r|complex number}}
  224 bytes (27 words) - 11:52, 29 November 2008
• Fundamental Theorem of Algebra/Related Articles
  {{r|Complex number}}
  493 bytes (64 words) - 16:43, 11 January 2010
• Commutativity
  ...cation]] of [[integer]]s, [[rational number]]s, [[real number|real]] and [[complex number]]s. In this context commutativity is often referred to as the ''commutativ
  695 bytes (102 words) - 19:40, 31 January 2009
• Zero (mathematics)
  a real number (with the decimal expansion 0.000...), and a complex number (0+0i).
  2 KB (326 words) - 18:28, 17 July 2009
• Distributivity/Related Articles
  {{r|Complex number}}
  626 bytes (79 words) - 16:01, 11 January 2010
• Ordered pair/Related Articles
  {{r|Complex number}}
  592 bytes (77 words) - 19:15, 11 January 2010
• Polynomial/Related Articles
  {{r|Complex number}}
  2 KB (206 words) - 19:38, 11 January 2010
• Quadratic equation/Related Articles
  {{r|complex number}}
  199 bytes (24 words) - 11:54, 4 December 2008
• Field (mathematics)
  ...</math>, the set of real numbers and <math>\mathbb{C}</math>, the set of [[complex number|complex numbers]].
  3 KB (496 words) - 22:16, 7 February 2010
• Pole (complex analysis)
  ...a type of [[singularity]] of a [[function (mathematics)|function]] of a [[complex number|complex]] variable. In the neighbourhood of a pole, the function behave li
  1 KB (188 words) - 13:32, 8 March 2009
• Taylor series/Related Articles
  {{r|Complex number}}
  993 bytes (129 words) - 20:50, 11 January 2010
• Cubic equation/Related Articles
  {{r|complex number}}
  317 bytes (40 words) - 00:19, 11 December 2008
• Discriminant of an algebraic number field
  ...n makes use of the ''n'' different embeddings of ''K'' into the field of [[complex number]]s '''C''', say σ₁, ...,σ_''n'':
  1 KB (235 words) - 01:20, 18 February 2009
• Norm (mathematics)
  Let ''X'' be a vector space over some subfield ''F'' of the [[complex number|complex numbers]]. Then a norm on X is any function <math>\|\cdot\|:X \righ
  880 bytes (157 words) - 22:28, 20 February 2010
• Banach space
  ...>\scriptstyle 1\, \leq p \,\leq\, \infty</math>, denote the space of all [[complex number|complex]]-valued measurable functions on the unit circle <math>\scriptstyle
  2 KB (317 words) - 13:13, 14 July 2008
• Field automorphism
  * The field '''C''' of [[complex number]]s has two automorphisms, the identity and [[complex conjugation]].
  3 KB (418 words) - 12:18, 20 December 2008
• Prime Number Theorem
  ...used to extend the definition to all values of <math>s</math>, including [[complex number]]s. The function with the extended domain is known as the [[Riemann zeta fu
  4 KB (703 words) - 12:02, 13 November 2007
• Complex analysis
  ...lysis''' is, broadly speaking, the study of functions that take as input [[complex number]]s and output complex numbers, and behave well with respect to a notion of ...ed to keep in mind that <math>| \cdot |</math> represents the modulus of a complex number, not the real absolute value.
  6 KB (1,077 words) - 19:25, 29 September 2020
• Kinematics/Related Articles
  * ''Quaternion'': an extension of a complex number having more than one imaginary component.
  471 bytes (59 words) - 05:36, 9 January 2024
• Cubic equation
  ...utions for which the cubic formula requires one to calculate a root of a [[complex number]]. This is more difficult than finding the root of a real number, which is
  3 KB (483 words) - 23:24, 17 December 2008
• Biholomorphism
  A [[linear function]] is a function <math>f</math> such that there exist [[complex number]]s
  2 KB (293 words) - 17:36, 25 January 2009
• Abelian group
  ...he [[integer]]s, the [[rational number]]s, the [[real number]]s, and the [[complex number]]s are abelian groups with the group operation being addition. In contrast
  2 KB (240 words) - 10:48, 21 September 2013
• Matrix inverse
  ...over a [[field (mathematics)|field]] such as the [[real number|real]] or [[complex number]]s, this is equivalent to specifying that the determinant does not equal ze
  1 KB (158 words) - 00:36, 18 April 2009
• Root of unity
  ...It is often convenient to identify the ''n''-th roots of unity with the [[complex number]]s exp(2πi.''r''/''n'') with ''r''=0,...,''n''-1 and the primitive ''n''-t
  1 KB (197 words) - 22:01, 7 February 2009
• Power series
  ...y consider power series in a complex variable <math>z-a</math> for a fixed complex number ''a''.
  4 KB (785 words) - 14:27, 14 March 2021
• Scale/Related Articles
  {{r|Complex number}}
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• Entire function
  [[modulus of complex number|modulus]], [[argument of complex number|argument]],
  6 KB (827 words) - 14:44, 19 December 2008
• Algebraic number
  ...specifically&mdash;in [[number theory]], an '''algebraic number''' is a [[complex number]] that is a root of a [[polynomial]] with [[rational number|rational]] coef ...s. It follows that the term "algebraic number" can also be defined as a [[complex number]] that is a root of a [[polynomial]] with [[integer]] coefficients. If an
  7 KB (1,145 words) - 00:49, 20 October 2013
• Adjoint (operator theory)
  ...the Hermitian conjugate of a complex [[matrix]] to linear operators on [[complex number|complex]] [[Hilbert space|Hilbert spaces]]. In this article the adjoint of The fact that the complex conjugate of the complex number ''a'' appears is due to the property of the inner product on complex Hilber
  5 KB (914 words) - 08:41, 17 October 2009
• Triangle inequality/Related Articles
  {{r|Complex number}}
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• Octonions/Related Articles
  {{r|Complex number}}
  489 bytes (62 words) - 19:09, 11 January 2010
• Fundamental Theorem of Algebra
  ...whose coefficients are [[Complex number|complex numbers]] has at least one complex number as a root. In other words, given any polynomial (where <math>d</math> is any positive integer), we can find a complex number <math>t</math> so that
  5 KB (924 words) - 16:35, 11 December 2008
• Cauchy-Schwarz inequality
  Let ''V'' be a [[complex number|complex]] [[inner product space]] with inner product <math>\langle \cdot,\c ...of vectors in ''V'' and let <math>\phi(x,y)</math> be the argument of the complex number <math>\langle x,y\rangle</math>. Now, consider the expression <math>f(t)=\l
  4 KB (629 words) - 16:46, 17 December 2008
• Quaternions/Related Articles
  {{r|Complex number}}
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• Cauchy-Riemann equations
  ...dition between the [[Real part|real]] and [[imaginary part]] of a given [[Complex number|complex valued]] function of <var>2n</var> [[real number|real]] [[variable] ..., <var>y</var>) + <var>i</var><var>v</var>(<var>x</var>, <var>y</var>) a [[Complex number|complex valued]] [[differentiable function]]. Then <var>f</var> satisfies t
  6 KB (874 words) - 03:45, 7 October 2013
• Polar coordinates/Related Articles
  {{r|Complex number}}
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• Algebraic number field
  We may embed ''K'' into the [[algebraically closed field]] of [[complex number]]s '''C'''. There are exactly ''n'' such embeddings: we can see this by ta
  7 KB (1,077 words) - 17:18, 10 January 2009
• Complex number/Advanced
  ...r by [[William Rowan Hamilton]] in 1837; this construction is explained [[Complex number#Formal definition|later in this article]].
  4 KB (685 words) - 00:41, 6 May 2008
• Eigenvalue
  and in general <math>\lambda</math> can be [[complex number|complex]].
  4 KB (731 words) - 17:16, 11 December 2008
• Cubic reciprocity
  ...ssed in terms of the [[Eisenstein integer]]s, that is, the ring ''E'' of [[complex number]]s of the form
  2 KB (319 words) - 15:45, 27 October 2008
• Polynomial ring/Related Articles
  {{r|Complex number}}
  770 bytes (96 words) - 19:39, 11 January 2010
• Erlang (programming language)/Tutorials/erlangOOP
  ...iagram. An integer is a Real. A Real(float) is a (subset of) complex. An a complex number is a (subset of) complex matrices, if we think of a (1 by 1) matrix as a si
  9 KB (1,125 words) - 07:07, 8 August 2009
• Commutativity/Related Articles
  {{r|Complex number}}
  858 bytes (112 words) - 15:35, 11 January 2010
• Holomorphic function
  ...functions]] defined on an [[open set|open subset]] of the [[complex number|complex number plane]] <math>\mathbb{C}</math> with values in <math>\mathbb{C}</math> that
  9 KB (1,434 words) - 15:35, 7 February 2009
• Riemann zeta function
  ...iemann|Riemann]] zeta function is a [[meromorphic function]] defined for [[complex number]]s with [[real part]] <math>\scriptstyle \Re(s) > 1</math> by the [[infinit
  7 KB (1,113 words) - 10:50, 4 October 2013
• Euclidean geometry/Related Articles
  {{r|Complex number}}
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• Character (group theory)
  ...orphism]] from ''G'' to the [[unit circle]], the multiplicative group of [[complex number]]s of [[modulus]] one.
  680 bytes (98 words) - 06:19, 15 June 2009
• Associativity
  ...cation]] of [[integer]]s, [[rational number]]s, [[real number|real]] and [[complex number]]s. In this context associativity is often referred to as the ''associativ
  2 KB (295 words) - 14:56, 12 December 2008
• Isogeny
  An elliptic curve over the [[complex number]]s is isomorphic to a quotient of the complex numbers by some [[lattice (ge
  4 KB (647 words) - 15:51, 7 February 2009
• Quaternions
  ...eed for quaternions became apparent after the successful introduction of [[Complex number|complex numbers]] into mathematics. These numbers made it possible to add, ...a real number can be interpreted as a point in 1-dimensional space, and a complex number can be interpreted as a point in 2-dimensional space, a quaternion may be i
  7 KB (1,160 words) - 07:41, 22 December 2008
• Self-adjoint operator
  ...ator''' is a [[denseness|densely]] defined [[linear operator]] mapping a [[complex number|complex]] [[Hilbert space]] onto itself and which is invariant under the un
  4 KB (709 words) - 06:58, 23 December 2008
• Complex conjugation/Related Articles
  {{r|Complex number}}
  873 bytes (139 words) - 12:36, 20 November 2008
• Complex number
  ...unter complex numbers when solving [[quadratic equation]]s, which can have complex number solutions. This presentation is historically misleading — the quadratic ...squares are negative. A historical example of this can be found on the [[Complex number/Advanced|"advanced" subpage]] for this article.
  18 KB (3,028 words) - 17:12, 25 August 2013
• Ordered pair
  ...' and ''y'' in ''Y'' is the [[Cartesian product]] of ''X'' and ''Y''. A [[complex number]] may be expressed as an ordered pair of [[real number]]s, the real and ima
  1 KB (213 words) - 07:01, 21 January 2009
• Exponential function
  where <math>\mathbb{C}</math> means the set of [[complex number]]s.
  6 KB (1,021 words) - 12:18, 11 June 2009
• Number
  ...one being <math> \scriptstyle \sqrt{-1} = (0, 1) = i </math>). Because the complex number set is [[algebraically closed]], it finds applications in many scientific f ...des all rational numbers and a subset of the irrational numbers. Any other complex number is a [[transcendental number]].
  11 KB (1,701 words) - 20:07, 1 July 2021
• Schrödinger equation/Related Articles
  {{r|Complex number}}
  1 KB (143 words) - 10:13, 9 May 2011
• Exponent
  ...including [[negative integer]]s, [[rational number]]s, [[real number]]s, [[complex number]]s, and even [[matrix|matrices]], [[set (mathematics)|set]]s, and other mor
  8 KB (1,297 words) - 14:49, 12 December 2008
• Inner product
  Let ''X'' be a vector space over a [[field|sub-field]] ''F'' of the [[complex number|complex numbers]]. An inner product <math>\langle \cdot,\cdot \rangle</math
  3 KB (511 words) - 00:25, 20 February 2010
• Complex number/Citable Version
  ...r by [[William Rowan Hamilton]] in 1837; this construction is explained [[Complex number#Formal definition|later in this article]]. ...i</math>. In this way, the real number <math>a</math> is considered as the complex number <math>a + 0i</math> whose imaginary part is zero.
  20 KB (3,304 words) - 17:11, 25 August 2013
• Equation (mathematics)
  ...s]], while unknown variables <math>x</math> are [[real number|real]] or [[complex number|complex]] numbers.
  6 KB (951 words) - 05:01, 8 December 2009
• Holomorphic function/Proofs
  In [[complex analysis]], a field of [[mathematics]], a [[complex number|complex]]-valued [[function (mathematics)|function]] ''f'' of a complex var
  4 KB (730 words) - 15:17, 8 December 2009
• Field extension
  For example, the field of [[complex number]]s '''C''' is an extension of the field of [[real number]]s '''R'''.
  3 KB (435 words) - 22:38, 22 February 2009
• Scalar
  ...ysics]], the word '''scalar''' is often used to refer simply to a real or complex number. ...matrix|rotation]]). The [[determinant]] of a unitary transformation is a complex number of absolute value unity, that is, the determinant of a unitary transformati
  9 KB (1,373 words) - 06:21, 11 December 2009
• Quadratic equation
  ...d to work for all quadratic polynomials, but sometimes the roots will be [[complex number]]s even when every other part of the problem deals only with [[real number
  8 KB (1,360 words) - 16:44, 17 December 2008
• Polynomial
  ...governed by [[modular arithmetic|arithmetic modulo 2]]. Polynomials with complex number coefficients or coefficients modulo 2 behave similarly to polynomials with
  8 KB (1,242 words) - 02:01, 10 November 2009
• Fourier transform
  Given some [[complex number|complex-valued]] function <math>\scriptstyle f\,:\,\mathbb{R} \rightarrow \
  3 KB (547 words) - 07:21, 24 December 2008
• Complex number/Approval
  Created [[Complex number/Draft]] [[User:David Tribe|David Tribe]] 19:30, 6 May 2007 (CDT)
  2 KB (190 words) - 10:10, 26 December 2009
• Multiplication
  ...ext of real numbers. There are natural multiplication operations on the [[complex number]]s, [[matrix|matrices]], [[tensor]]s, [[sequence]]s, and [[function]]s.
  5 KB (638 words) - 14:16, 17 December 2008
• Continuity
  This definition of continuity extends directly to functions of a [[complex number|complex]] variable.
  3 KB (614 words) - 14:20, 13 November 2008
• Algebraic geometry
  ...the ground field has been extended from the real numbers to the field of [[complex number]]s and later to arbitrary [[field]]s. In the second place notions of abstra
  2 KB (287 words) - 10:43, 11 June 2009
• Polynomial/Advanced
  ...like [[integer]]s, [[rational number|rational]], [[real number|real]] or [[complex number|complex]] numbers. Still it is important to understand that calculations wi
  10 KB (1,741 words) - 10:04, 3 January 2009
• Iteration of function
  ...ath> and <math>G</math> are established, the function can be iterated even complex number of times. ...omorphic function can be iterated any number <math>n</math> of times, even complex number of times.
  15 KB (2,340 words) - 08:27, 9 September 2020
• Polynomial equation
  ...d, but applying them requires sophisticated knowledge of arithmetic with [[complex number]]s. There are no analogous formulas for solving polynomial equations of or
  4 KB (647 words) - 16:35, 22 December 2008
• Sequence
  Some simple examples of sequences of the natural, [[real numbers|real]], or [[complex number]]s include (respectively)
  2 KB (270 words) - 15:56, 12 November 2008
• Ring (mathematics)
  **The [[rational number|rational]], [[real number|real]] and [[complex number|complex]] numbers each form commutative rings.
  10 KB (1,667 words) - 13:47, 5 June 2011
• Fourier series
  In the case of a [[complex number|complex]]-valued function ''ƒ''(&xi;), ''Fourier's theorem'' states that a
  7 KB (1,088 words) - 10:11, 11 June 2012
• Group theory
  However, over the [[complex number]]s we can write
  15 KB (2,535 words) - 20:29, 14 February 2010
• Galois theory
  Galois expressed his theory in terms of polynomials and [[complex number|complex numbers]], today Galois theory is usually formulated using general
  4 KB (683 words) - 22:17, 7 February 2010
• Cubic equation/Proofs
  ...ressed in radicals using only real numbers. But finding the cube root of a complex number can be accomplished in polar form, so changing the form of the complex numb
  8 KB (1,339 words) - 11:08, 15 September 2009
• Heaviside step function
  In order to prove the last relation we write a complex number in polar form
  5 KB (796 words) - 13:09, 24 December 2008
• Logarithm
  ...value of <math>f(x)</math> within the [[real number]]s &mdash; but using [[complex number]]s a value can be found, as will be discussed further below. To find the logarithm of a complex number <math>a + bi</math>, it is convenient to express the number in polar coordi
  19 KB (3,039 words) - 12:51, 7 March 2023
• Real number
  ...tended in several directions. Perhaps the most natural extension are the [[complex number]]s, which contain solutions to all [[polynomial]] equations, and, unlike th
  19 KB (2,948 words) - 10:07, 28 February 2024
• Lambert W function
  for any [[complex number]] <math>\scriptstyle z</math>. Equivalently, it may be defined as the [[inv
  14 KB (2,354 words) - 21:43, 25 September 2011
• Thévenin's theorem
  ...upon frequency, as normally expressed using an impedance represented by a complex number.
  7 KB (1,223 words) - 11:22, 26 May 2011
• Benjamin Peirce
  ...1843 theory of [[quaternions]]. The quaternions are a generalization of [[complex number]]s. They can be added and multiplied and thus form a structure that is now
  8 KB (1,209 words) - 08:09, 28 September 2013
• Vector space
  ...math>\mathbb{R}^n</math></font> for any [[natural number]] ''n''; or the [[complex number|complex plane]] or powers of it, <font style = "vertical-align: 13%"><math
  15 KB (2,506 words) - 05:16, 11 May 2011
• Number theory
  ...lisations of the rational numbers. Briefly, an ''algebraic number'' is any complex number that is a solution to some polynomial equation <math>\scriptstyle f(x)=0</m
  27 KB (4,383 words) - 08:05, 11 October 2011
• Clebsch-Gordan coefficients
  ...th>, where <math>\scriptstyle c^*\,</math> is the complex conjugate of the complex number ''c''.
  11 KB (1,759 words) - 10:02, 2 August 2008
• Euler's theorem (rotation)
  ...theory must be recalled. Matrices over the [[field (algebra)|field]] of [[complex number]]s are considered.
  12 KB (1,865 words) - 02:49, 19 April 2010
• Algebra
  ...mathbb{Q}</math> (also [[Real numbers|real]] <math>\mathbb{R}</math> and [[Complex number|complex]] <math>\mathbb{C}</math> numbers)
  18 KB (2,669 words) - 08:38, 17 April 2024
• Module
  ...encountered in applications or linear algebra courses usually use real or complex number scalars, the most general type of vector space is a module over a [[divisio
  7 KB (1,154 words) - 02:39, 16 May 2009
• Set (mathematics)
  *<math>\mathbb{C}</math>, the set of [[complex number|complex numbers]]
  17 KB (2,828 words) - 10:37, 24 July 2011
• Newton's method
  Newton's method also works in the [[complex number]]s; for example, it can be used to find complex roots of polynomials. Its b
  17 KB (2,889 words) - 12:40, 11 June 2009
• Measure (mathematics)
  ...alled a ''[[signed measure]]'', while such a function with values in the [[complex number]]s is called a ''[[complex measure]]''. Measures that take values in [[Bana
  14 KB (2,350 words) - 17:37, 10 November 2007
• Space (mathematics)
  An object parametrized by ''n'' [[complex number]]s may be treated as a point of a complex ''n''-dimensional space. However, ...ce (the latter ''underlies'' the former), since each real number is also a complex number. Linear operations, given in a linear space by definition, lead to such not
  28 KB (4,311 words) - 08:36, 14 October 2010
• Lie algebra
  ...that these form only a real Lie algebra, as multiplication with a general complex number does not preserve skew-hermiticity.
  12 KB (1,918 words) - 20:29, 22 December 2011
• Gamma function
  ..., "positive" will be understood to mean either a positive real number or a complex number with positive real part.</ref> ...t comes arbitrarily close as <math>z\to-\infty</math>. There is in fact no complex number ''z'' for which <math>\Gamma(z) = 0</math>, and hence the ''reciprocal gamm
  32 KB (5,024 words) - 12:05, 22 December 2008
• Series (mathematics)
  ...> a_n \cos nx + b_n \sin nx </math>; the latter being the real part of the complex number <math> c_n e^{inx} </math> for <math> c_n = a_n - i b_n </math>, the series
  19 KB (3,369 words) - 02:33, 13 January 2010
• Superfunction
  Chose a [[complex number]] <math>c</math> and define function
  21 KB (3,134 words) - 09:12, 10 October 2013
• Trigonometric function
  ...]s, allowing their extension to positive and negative values and even to [[complex number]]s. All of these approaches will be presented below. ...n from the series definitions that the sine and cosine functions are the [[complex number|imaginary]] and real parts, respectively, of the [[exponential function|com
  33 KB (5,179 words) - 08:26, 4 June 2010
• Group (mathematics)
  ...he [[integer]]s, the [[rational number]]s, the [[real number]]s, and the [[complex number]]s under addition, as well as the non-zero rationals, reals, and complex nu
  19 KB (3,074 words) - 11:11, 13 February 2009
• Z (letter)
  *''z'': generic symbol for a complex number
  4 KB (700 words) - 15:40, 4 April 2017
• Function (mathematics)
  ...alyse them. Many of these properties are also meaningful with respect to [[complex number|complex]] functions and functions of several variables.
  15 KB (2,342 words) - 06:26, 30 November 2011
• Simon Stevin
  ...ch are [[irrational number]]s), and negative numbers. He did not accept [[complex number]]s.
  8 KB (1,266 words) - 03:23, 27 April 2010
• Norton's theorem
  ...upon frequency, as normally expressed using an impedance represented by a complex number.
  9 KB (1,673 words) - 11:24, 26 May 2011
• Augustin-Louis Cauchy
  ...alytic on ''C'' and within the region bounded by the contour ''C'' and the complex number ''a'' is somewhere in this region. The contour integral is taken counter-cl
  20 KB (3,286 words) - 12:52, 24 August 2013
• Bode plot
  Using the rules for [[complex number]]s, the magnitude of this gain expression is plotted on the Bode gain plot: where vertical bars denote the magnitude of a complex number (for example, | a + j b | = [ a² + b²]^1/2
  24 KB (3,933 words) - 02:20, 14 October 2013
• Augustin-Louis Cauchy/Citable Version
  ...alytic on ''C'' and within the region bounded by the contour ''C'' and the complex number ''a'' is somewhere in this region. The contour integral is taken counter-cl
  20 KB (3,295 words) - 12:51, 24 August 2013
• CZ Talk:Request Approved Article Copyedit/Archive 1
  ...zendium.org/wiki?title=Complex_number/Draft&diff=100636845&oldid=100613762 Complex number]
  10 KB (1,384 words) - 11:05, 26 November 2014
• CZ Talk:Formatting mathematics
  ...bold and write <math>\Delta=\left(22\sqrt{-1}\right)^2</math>. '' (from [[Complex number]], try to resize). The point is that, generally, a punctuation mark at the
  12 KB (2,084 words) - 15:38, 11 February 2008
• Sine
  ...are also [[real number]]s. However, the definition above can be used for [[complex number]]s too.
  19 KB (3,106 words) - 09:53, 10 October 2013
• Mathematics
  ...used to represent continuous quantities. Real numbers are generalised to [[complex number]]s. These are the first steps of a hierarchy of number systems that include ...number]]s|| [[Integer]]s || [[Rational number]]s || [[Real number]]s || [[Complex number]]s
  30 KB (4,289 words) - 16:03, 20 January 2023
• Quantum mechanics/Advanced
  ...quantum mechanics, the state of a system at a given time is described by [[complex number|complex]] [[wave functions]] (sometimes referred to as orbitals in the case ...ace" or the "associated Hilbert space" of the system) well defined up to a complex number of norm 1 (the phase factor). In other words, the possible states are point
  37 KB (5,578 words) - 04:54, 21 March 2024
• Internal-external distinction
  ...y unit]] √−1 ''might'' be an internal question framed in the language of [[complex number]]s about the correct usage of √−1, or it ''might'' be a question about
  22 KB (3,436 words) - 22:46, 28 July 2013
• CZ Talk:Mathematics Workgroup
  : It has been pointed out that markup has its advantages, see [[Talk:Complex number#Comments]] (and also [http://forum.citizendium.org/index.php/topic,860.msg6
  44 KB (7,312 words) - 03:09, 8 March 2024
• Sturm-Liouville theory
  where ''z'' is chosen to be some complex number which is not an eigenvalue. Then, computing the resolvent amounts to solvin
  15 KB (2,332 words) - 04:52, 18 October 2009
• CZ Talk:Approval Announcements
  ...have clearly rendered their opinion. This was exactly what took place in [[Complex number]].[[User:Nancy Sculerati|Nancy Sculerati]] 14:29, 16 May 2007 (CDT)
  28 KB (4,664 words) - 19:11, 4 November 2008
• CZ Talk:Approval Process
  ...number]], as directed, the "articles to approve" special page lists [[Talk:Complex number]] as the one needing approval. Code glitch? or did I do it wrong? - [[User: ...have clearly rendered their opinion. This was exactly what took place in [[Complex number]].[[User:Nancy Sculerati|Nancy Sculerati]] 14:29, 16 May 2007 (CDT)
  96 KB (16,369 words) - 10:49, 7 March 2024