# Fungrim entry: ec7f2d

$\operatorname{atan}(z) = \operatorname{csgn}(z) \operatorname{acos}\!\left(\frac{1}{\sqrt{1 + {z}^{2}}}\right)$
Assumptions:$z \in \mathbb{C} \setminus \left\{-i, i\right\}$
TeX:
\operatorname{atan}(z) = \operatorname{csgn}(z) \operatorname{acos}\!\left(\frac{1}{\sqrt{1 + {z}^{2}}}\right)

z \in \mathbb{C} \setminus \left\{-i, i\right\}
Definitions:
Fungrim symbol Notation Short description
Atan$\operatorname{atan}(z)$ Inverse tangent
Csgn$\operatorname{csgn}(z)$ Real-valued sign function for complex numbers
Sqrt$\sqrt{z}$ Principal square root
Pow${a}^{b}$ Power
CC$\mathbb{C}$ Complex numbers
ConstI$i$ Imaginary unit
Source code for this entry:
Entry(ID("ec7f2d"),
Formula(Equal(Atan(z), Mul(Csgn(z), Acos(Div(1, Sqrt(Add(1, Pow(z, 2)))))))),
Variables(z),
Assumptions(Element(z, SetMinus(CC, Set(Neg(ConstI), ConstI)))))

## Topics using this entry

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

2020-01-31 18:09:28.494564 UTC