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Fungrim entry: 632063

atan ⁣(z)=atan ⁣(z)\operatorname{atan}\!\left(\overline{z}\right) = \overline{\operatorname{atan}\!\left(z\right)}
Assumptions:zCandiz(,1)(1,)z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, i z \notin \left(-\infty, -1\right) \cup \left(1, \infty\right)
TeX:
\operatorname{atan}\!\left(\overline{z}\right) = \overline{\operatorname{atan}\!\left(z\right)}

z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, i z \notin \left(-\infty, -1\right) \cup \left(1, \infty\right)
Definitions:
Fungrim symbol Notation Short description
Atanatan ⁣(z)\operatorname{atan}\!\left(z\right) Inverse tangent
Conjugatez\overline{z} Complex conjugate
CCC\mathbb{C} Complex numbers
ConstIii Imaginary unit
OpenInterval(a,b)\left(a, b\right) Open interval
Infinity\infty Positive infinity
Source code for this entry:
Entry(ID("632063"),
    Formula(Equal(Atan(Conjugate(z)), Conjugate(Atan(z)))),
    Variables(z),
    Assumptions(And(Element(z, CC), NotElement(Mul(ConstI, z), Union(OpenInterval(Neg(Infinity), -1), OpenInterval(1, Infinity))))))

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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-09-16 21:17:18.797188 UTC