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Fungrim entry: 9dec3e

atan2 ⁣(y,x)=ilog ⁣(sgn ⁣(x+yi))\operatorname{atan2}\!\left(y, x\right) = -i \log\!\left(\operatorname{sgn}\!\left(x + y i\right)\right)
Assumptions:xRandyRandx+yi0x \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) = -i \log\!\left(\operatorname{sgn}\!\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
ConstIii Imaginary unit
Loglog ⁣(z)\log\!\left(z\right) Natural logarithm
Signsgn ⁣(z)\operatorname{sgn}\!\left(z\right) Sign function
RRR\mathbb{R} Real numbers
Source code for this entry:
Entry(ID("9dec3e"),
    Formula(Equal(Atan2(y, x), Mul(Neg(ConstI), Log(Sign(Add(x, Mul(y, ConstI))))))),
    Variables(x, y),
    Assumptions(And(Element(x, RR), Element(y, RR), Unequal(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.

2019-09-19 20:12:49.583742 UTC