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{{short description|Space formed by the ''n''-tuples of complex numbers}} ...and is the ''n''-fold [[Cartesian product]] of the [[complex line]] <math>\Complex</math> with itself. Symbolically, ...

...[[complex number]]s, and [[complete valued field]]s (such as the [[p-adic numbers|''p''-adic number]]s). ===Real and complex numbers=== ...

...thematics)|characterizes]] the [[gamma function]], defined for all complex numbers <math>z</math> for which <math>\mathrm{Re}\,z > 0</math> by ...nly function <math>f</math> defined on the half-plane <math>H := \{ z \in \Complex : \operatorname{Re}\,z > 0\}</math> such that: ...

...RiemannKugel.svg|thumb|right|The [[Riemann sphere]] is one of the simplest complex algebraic varieties.]] ...], and [[Igor Rostislavovich Shafarevich]], eds. ''Algebraic Geometry III: Complex Algebraic Varieties. Algebraic Curves and Their Jacobians.'' Vol. 3. Spring ...

...(mathematics)|field]] {{Harv|Artin|1966}}, usually the field of [[complex numbers]]. If ''G'' is any group, then the [[Set (mathematics)|set]] Ch(''G'') of 0 & 1 \end{pmatrix}\right)=a^u,</math> where ''u'' ranges over complex numbers '''C''' are multiplicative characters. ...

In [[complex analysis]], a mathematical discipline, the '''fundamental normality test''' ...defined on a domain <math> \Omega </math>. If there are two fixed complex numbers ''a'' and ''b'' such that for all ''&fnof;''&nbsp;&isin;&nbsp;<math>\mathca ...

...]] and <math>\mathbb K</math> either the [[real numbers]] or the [[complex numbers]], such that for any given <math>f \in \mathcal C(X, \mathbb K)</math> ther ...

...generalizes the concepts of [[reflection (mathematics)|reflection]] and [[complex reflection]] and is simply called '''reflection''' by some mathematicians. ...characteristic zero, such as the field of real numbers and the field of [[complex number]]s. ...

{{short description|Algebra of eight complex dimensions}} In [[mathematics]], a '''bioctonion''', or '''complex octonion''', is a pair (''p,q'') where ''p'' and ''q'' are [[biquaternion]] ...

...mathematics]], a '''complex Lie algebra''' is a [[Lie algebra]] over the [[complex number]]s. ...d only if]] it admits a real form (and is said to be defined over the real numbers). ...

...nce involves functions of a [[motor variable]] where arguments are [[split-complex number]]s. ...ical space|topology]] of the [[space (mathematics)|space]] of hypercomplex numbers determines the function theory. Functions such as [[square root of a matrix ...

In [[mathematics]], the '''complex squaring map''', a [[polynomial]] mapping of [[degree of a polynomial|degre # Choose any [[complex number]] on the [[unit circle]] whose [[Complex_number#Polar_complex_plane| ...

...eve]]. It may be used to extend [[Rolle's theorem]] from real functions to complex functions, taking the role that for real functions is played by the number ...complex-valued function ''f'' that is [[analytic function|analytic]] in a complex [[Neighbourhood (mathematics)|neighbourhood]] of the real interval <math>I< ...

...'</sub>) of [[real numbers]] <math>\R</math> or [[complex numbers]] <math>\Complex</math> such that ...

...h in turn guarantees that the combined operator's eigenvalues will be real numbers, suitable for predicting values of observations / measurements.<ref name=Öz ...conjugate transpose]]'') of <math>A</math>, defined as applying both the [[complex conjugate]] and the [[transpose]] transformations to the operator <math>A</ ...

...s, '''Turán's method''' provides lower bounds for [[exponential sum]]s and complex [[power sum]]s. The method has been applied to problems in [[equidistribut ...ntegers. There are two main results, depending on the size of the complex numbers&nbsp;''z''. ...

...p. For example, if ''X'', ''Y'' are [[manifold]]s, ''R'' the field of real numbers, and the cohomology is [[de Rham cohomology]], then the pullback is induced ...al of a [[chain complex]]. Let ''R'' be a commutative ring, ''C'' a chain complex of ''R''-[[module (mathematics)|modules]] and ''G'' an ''R''-module. Just a ...

...lliptic curves over <math>R</math>. Since elliptic curves over the complex numbers are isomorphic (over an algebraic closure) if and only if their <math>j</ma ...ication]] by <math>\mathbb{Z}[\zeta_3]</math>, and <math>j=1728</math> has complex multiplication by <math>\mathbb{Z}[i]</math>. ...

...of a [[Holomorphic function|holomorphic]] [[vector field]] of a compact [[complex manifold]]. If ''v'' is a holomorphic vector field on a compact complex manifold ''M'', then ...

...ich is causing the spikes in the left half of the graph (these are [[Pole (complex analysis)|simple poles]] of the function, where its values increase to [[in ...