# complex analysis

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complex analysis
the branch of mathematics dealing with analytic functions of a complex variable.

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Universalium. 2010.

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• Complex analysis — Plot of the function f(x)=(x2 1)(x 2 i)2/(x2 + 2 + 2i). The hue represents the function argument, while the brightness represents the magnitude. Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch …   Wikipedia

• complex analysis — Math. the branch of mathematics dealing with analytic functions of a complex variable …   Useful english dictionary

• complex analysis — noun The branch of mathematics that studies holomorphic functions …   Wiktionary

• List of complex analysis topics — Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematics that investigates functions of complex numbers. It is useful in many branches of mathematics, including number theory and applied …   Wikipedia

• Zero (complex analysis) — In complex analysis, a zero of a holomorphic function f is a complex number a such that f(a) = 0. Contents 1 Multiplicity of a zero 2 Existence of zeros 3 Properties …   Wikipedia

• Argument (complex analysis) — Arg (mathematics) redirects here. For argument of a function, see Argument of a function. Figure 1. This Argand diagram represents the complex numbers lying on a plane. For each point on the plane, arg is the function which returns the angle φ.… …   Wikipedia

• Residue (complex analysis) — In mathematics, more specifically complex analysis, the residue is a complex number proportional to the contour integral of a meromorphic function along a path enclosing one of its singularities. (More generally, residues can be calculated for… …   Wikipedia

• Pole (complex analysis) — The absolute value of the Gamma function. This shows that a function becomes infinite at the poles (left). On the right, the Gamma function does not have poles, it just increases quickly. In the mathematical field of complex analysis, a pole of a …   Wikipedia

• Antiderivative (complex analysis) — In complex analysis, a branch of mathematics, the antiderivative, or primitive, of a complex valued function g is a function whose complex derivative is g. More precisely, given an open set U in the complex plane and a function the antiderivative …   Wikipedia

• Open mapping theorem (complex analysis) — In complex analysis, the open mapping theorem states that if U is a connected open subset of the complex plane C and f : U → C is a non constant holomorphic function, then f is an open map (i.e. it sends open subsets of U to open subsets of… …   Wikipedia