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  2. Additive inverse - Wikipedia

    en.wikipedia.org/wiki/Additive_inverse

    In a vector space, the additive inverse −v (often called the opposite vector of v) has the same magnitude as v and but the opposite direction. [11] In modular arithmetic, the modular additive inverse of x is the number a such that a + x ≡ 0 (mod n) and always exists. For example, the inverse of 3 modulo 11 is 8, as 3 + 8 ≡ 0 (mod 11). [12]

  3. Zeros and poles - Wikipedia

    en.wikipedia.org/wiki/Zeros_and_poles

    More precisely, let f be a function from a complex curve M to the complex numbers. This function is holomorphic (resp. meromorphic) in a neighbourhood of a point z of M if there is a chart ϕ {\displaystyle \phi } such that f ∘ ϕ − 1 {\displaystyle f\circ \phi ^{-1}} is holomorphic (resp. meromorphic) in a neighbourhood of ϕ ( z ...

  4. Error function - Wikipedia

    en.wikipedia.org/wiki/Error_function

    Given a complex number z, there is not a unique complex number w satisfying erf w = z, so a true inverse function would be multivalued. However, for −1 < x < 1 , there is a unique real number denoted erf −1 x satisfying erf ⁡ ( erf − 1 ⁡ x ) = x . {\displaystyle \operatorname {erf} \left(\operatorname {erf} ^{-1}x\right)=x.}

  5. Argument (complex analysis) - Wikipedia

    en.wikipedia.org/wiki/Argument_(complex_analysis)

    Figure 1. This Argand diagram represents the complex number lying on a plane.For each point on the plane, arg is the function which returns the angle . In mathematics (particularly in complex analysis), the argument of a complex number z, denoted arg(z), is the angle between the positive real axis and the line joining the origin and z, represented as a point in the complex plane, shown as in ...

  6. List of complex analysis topics - Wikipedia

    en.wikipedia.org/wiki/List_of_complex_analysis...

    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 mathematics; as well as in physics, including hydrodynamics, thermodynamics, and electrical engineering.

  7. Antiderivative (complex analysis) - Wikipedia

    en.wikipedia.org/wiki/Antiderivative_(complex...

    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 in the complex plane and a function :, the antiderivative of is a function : that satisfies =.

  8. List of unsolved problems in mathematics - Wikipedia

    en.wikipedia.org/wiki/List_of_unsolved_problems...

    Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.

  9. Talk:Negative number - Wikipedia

    en.wikipedia.org/wiki/Talk:Negative_number

    The additive opposite of a number is unique, as is shown by the following proof. We define an additive opposite of a number as a value which when added to the number sums to zero. Let x be a number and let y be its additive opposite. Suppose y′ is another additive opposite of x. By definition: