Fungrim entry: 632063

\operatorname{atan}\!\left(\overline{z}\right) = \overline{\operatorname{atan}\!\left(z\right)}

Assumptions:

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
`Atan`	$\operatorname{atan}\!\left(z\right)$	Inverse tangent
`Conjugate`	$\overline{z}$	Complex conjugate
`CC`	$\mathbb{C}$	Complex numbers
`ConstI`	$i$	Imaginary unit
`OpenInterval`	$\left(a, b\right)$	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))))))

Topics using this entry

Inverse tangent