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Zero (complex analysis) (1183 bytes)
1: ...ero''' of a [[holomorphic function]] ''f'' is a [[complex number]] ''a'' such that ''f''(''a'') = 0. See a... 5: A complex number ''a'' is a '''simple zero''' of ''f'', or ... 16: ...real numbers are complex numbers, they still have complex zeroes). An example is ''f''(''x'') = ''x''<sup>... 20: [[Category:Complex analysis]] Complex analysis (5339 bytes) 1: ...ues, and are differentiable as complex functions. Complex differentiability has much stronger consequences ... 6: ...egrals, and here the theory of [[residue (complex analysis)|residue]]s among others is useful (see [[methods... 9: ... states that the [[field (mathematics)|field]] of complex numbers is [[algebraically closed field|algebraic... 11: ... function to a non-simply connected domain in the complex plane but it is possible to extend it to a holomo... 13: ... conformal relationship of certain domains in the complex plane, maybe the most important result in the one... Pole (complex analysis) (1836 bytes) 1: In [[complex analysis]], a '''pole''' of a [[function (mathematics)|fun... 3: ...lly, suppose ''U'' is an [[open subset]] of the [[complex plane]] '''C''', ''a'' is an element of ''U'' and... 9: ...b>''z''→''a''</sub> ''f''(''z'') exists as a complex number. If the order is bigger than 0, then lim<s... 18: * [[Zero (complex analysis)]] 21: [[Category:Complex analysis]] Residue (complex analysis) (4667 bytes) 1: [[Category:Complex analysis]] 2: In [[complex analysis]], the '''residue''' is a [[complex number]] which describes the behavior of [[path i... 25: ...''z'' : 0 < |''z'' − ''c''| < ''R''} in the complex plane is given and ''f'' is a [[holomorphic funct... 35: ... function around ''z'' = ''c'', a [[pole (complex analysis)|pole]] of order ''n'', one may use the following... List of complex analysis topics (2177 bytes) 1: This is a '''list of [[complex analysis]] topics''', by Wikipedia page. 15: *[[Pole (complex analysis)]] 16: *[[Zero (complex analysis)]] 17: *[[Residue (complex analysis)]] 36: *[[Liouville's theorem (complex analysis)]] Liouville's theorem (complex analysis) (2134 bytes) 1: [[Category:Complex analysis]][[Category:Theorems]] 2: ...ic function]] ''f''(''z'') defined on the whole [[complex plane]] '''C''') must be constant. 6: ...ry entire function whose image omits at least two complex numbers must be constant. 8: ...''M'' is a parabolic Riemann surface (such as the complex plane '''C''') and ''N'' is a hyperbolic one (suc... Complex (1289 bytes) 3: * A '''complex''' is a whole that comprehends a number of parts,... 5: * In [[psychology]], a '''[[complex (psychology)|complex]]''' is a group of mental factors that are uncons... 7: ...''', or '''coordination compound''' or '''[[metal complex]]''', is a structure consisting of a central [[at... 11: * A '''[[complex number]]''' is a number in the field of numbers w... 13: * A '''complex''' is an element of a '''[[complex algebra]]''' or [[field of sets]]. CW complex (6508 bytes) 1: ...lass of spaces that was broader than [[simplicial complex]]es (we could say now, had better [[category theo... 3: ...complement, the interior points. A general ''cell complex'' would be a topological space ''X'' that is cove... 7: ...e in determining the nature of the newly enlarged complex. For example, if ''D''<sup>2</sup> is glued onto... 9: ==CW complexes are defined inductively== 13: ..., it must be a [[discrete space]]. The general CW-complex definition can proceed by induction, using this a... Several complex variables (5003 bytes) 1: ...[function (mathematics)|function]]s of '''several complex variables''' is the branch of [[mathematics]] dea... 5: ...[tuple]]s of [[complex number]]s. As in [[complex analysis]], which is the case ''n'' = 1 but of a distinct ... 9: ...n't become a fully-fledged area in [[mathematical analysis]], since its characteristic phenomena weren't unc... 11: ...gral|contour]] (line) integrals over two separate complex variables should come to a [[double integral]] ov... 15: ...ormation theory]] of [[complex structure]]s and [[complex manifold]]s was described in general terms by [[K... Chain complex (3539 bytes) 3: In [[homological algebra]], a '''chain complex''' <math>(A_\bullet, d_\bullet)</math> is a seque... 14: ...plex is that of ''cochain complex''. A '''cochain complex''' <math>(A^\bullet, d^\bullet)</math> is a seque... 26: Chain complexes are mainly used to define [[homology (mathemati... 39: ...<math>H_\bullet(X)</math> is the homology of this complex; that is, 46: ...long with the exterior derivative are a [[cochain complex]]: Complex multiplication (2778 bytes) 1: ...t]] is said to have remarked that ''the theory of complex multiplication is the most beautiful part of math... 3: An example of an elliptic curve with complex multiplication is 7: ... θ is any non-zero complex number. Any such complex [[torus]] has the Gaussian integers as endomorphi... 15: ...omplex multiplication, in the sense that over the complex number field they are all found as such quotients... 17: ...It is known that, in a general sense, the case of complex multiplication is the hardest to resolve for the ... Complex sentence (905 bytes) 1: ...t one [[dependent clause]] is referred to as a '''complex sentence'''. The dependent clause is often introd... 14: ...dent. This is a [[compound sentence]] but not a [[complex sentence]]. 17: ...t clause (''"[which] you gave me"''). This is a [[complex-compound sentence]]. Complex conjugate (3417 bytes) 1: In [[mathematics]], the '''complex conjugate''' 2: of a [[complex number]] is given by changing the sign of the ima... 3: ...en is used also for the conjugate transpose. If a complex number is treated as a 1×1 vector, the nota... 7: ...is contains the multiples of ''i''. In this view, complex conjugation corresponds to reflection at the [[x-... 11: These properties apply for all complex numbers ''z'' and ''w'', unless stated otherwise. Complex geometry (1008 bytes) 2: ...], '''complex geometry''' is the application of [[complex number]]s to [[plane geometry]]. 4: ... coordinates]], it can be represented as a single complex number, which can be written at will in either re... 6: ...se involving angles, by means of [[complex number|complex algebra]]. Using [[Euler's formula]], 10: it is possible to represent any [[rotation]] as a complex number. 12: Complex numbers can therefore be used to advantage to sol... Complex representation (702 bytes) 1: ... complex matrices, and the complex conjugate of a complex representation is a different, non-equivalent rep... 3: ...reater than two is a complex representation whose complex conjugate is often called the [[antifundamental r... Complex family (1401 bytes) 1: '''Complex Family''' is a generic term for any family struct... 3: A '''joint family''' is also known as a ''complex family'', parents and their children's families o... Sexual complex (95 bytes) 2: A psychological complex involving fixations of a sexual nature; "fetish" Polypyridine complex (1754 bytes) 1: '''Polypyridine complexes''' are compounds in which a polypyridine, such ... 3: ...tal charge transfer (LMCT). The properties of the complexes can be tuned easily by introducing substituents... 5: ...o the square planar structure of the [[platinum]] complex. Complex system (5457 bytes) 1: ... take account of the kinds of complexity found in complex systems. 3: ==Features of complex systems== 6: ...nts. [[Emergence]] is perhaps the key property of complex systems and a lot of work is being done to try to... 9: ...ypically, the relationships between elements in a complex system are short-range, that is [[information]] i... 17: ...r relationships lies at the heart of what makes a complex system special. Persecution complex (225 bytes) 1: ...'' is a term given to an array of psychologically complex behaviours, that specifically deals with the [[pe...
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