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{{r|Complex number}}

...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

...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

: (Jul 2009): [[Complex number]] (E,reapproval)

{{r|Complex number}}

...orphism]] from ''G'' to the [[unit circle]], the multiplicative group of [[complex number]]s of [[modulus]] one.

...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

...at fortunate as in the general case it requires finding the cube root of a complex number, which is not a straightforward operation like the square root. In fact it :: "It" is taking the cube root of a complex number. You can solve the general quadratic with real coefficients by "simple" ari

An elliptic curve over the [[complex number]]s is isomorphic to a quotient of the complex numbers by some [[lattice (ge

...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

...ator''' is a [[denseness|densely]] defined [[linear operator]] mapping a [[complex number|complex]] [[Hilbert space]] onto itself and which is invariant under the un

{{r|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.

...' 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

where <math>\mathbb{C}</math> means the set of [[complex number]]s.

...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]].

{{r|Complex number}}

...including [[negative integer]]s, [[rational number]]s, [[real number]]s, [[complex number]]s, and even [[matrix|matrices]], [[set (mathematics)|set]]s, and other mor

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

{{r|Complex number}} His additions to related: Complex number - well, why not integer, rational, real, as well?