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Fungrim entry: eca4ce

atan2⁡ ⁣(y,x)=Im⁡ ⁣(log⁡ ⁣(x+yi))\operatorname{atan2}\!\left(y, x\right) = \operatorname{Im}\!\left(\log\!\left(x + y i\right)\right)
Assumptions:x∈R  and⁡  y∈R  and⁡  x+yi≠0x \in \mathbb{R} \;\mathbin{\operatorname{and}}\; y \in \mathbb{R} \;\mathbin{\operatorname{and}}\; x + y i \ne 0
TeX:
\operatorname{atan2}\!\left(y, x\right) = \operatorname{Im}\!\left(\log\!\left(x + y i\right)\right)

x \in \mathbb{R} \;\mathbin{\operatorname{and}}\; y \in \mathbb{R} \;\mathbin{\operatorname{and}}\; x + y i \ne 0
Definitions:
Fungrim symbol Notation Short description
Atan2atan2⁡ ⁣(y,x)\operatorname{atan2}\!\left(y, x\right) Two-argument inverse tangent
ImIm⁡(z)\operatorname{Im}(z) Imaginary part
Loglog⁡(z)\log(z) Natural logarithm
ConstIii Imaginary unit
RRR\mathbb{R} Real numbers
Source code for this entry:
Entry(ID("eca4ce"),
    Formula(Equal(Atan2(y, x), Im(Log(Add(x, Mul(y, ConstI)))))),
    Variables(x, y),
    Assumptions(And(Element(x, RR), Element(y, RR), NotEqual(Add(x, Mul(y, ConstI)), 0))))

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

2021-03-15 19:12:00.328586 UTC