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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
  163 bytes (26 words) - 05:12, 23 June 2008
• 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
• Complex number/Related Articles
  276 bytes (34 words) - 10:41, 21 April 2010

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 Number
  #REDIRECT [[Complex number]]
  28 bytes (3 words) - 15:30, 28 October 2007
• 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
• 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}}
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• 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}}
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• 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
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• Taylor series/Related Articles
  {{r|Complex number}}
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• 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}}
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• 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}}
  532 bytes (68 words) - 19:37, 11 January 2010
• 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}}
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• 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