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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:xR  and  yR  and  x+yi0x \in \mathbb{R} \;\mathbin{\operatorname{and}}\; y \in \mathbb{R} \;\mathbin{\operatorname{and}}\; x + y i \ne 0
\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
Fungrim symbol Notation Short description
Atan2atan2 ⁣(y,x)\operatorname{atan2}\!\left(y, x\right) Two-argument inverse tangent
ConstIii Imaginary unit
Loglog(z)\log(z) Natural logarithm
Signsgn(z)\operatorname{sgn}(z) Sign function
RRR\mathbb{R} Real numbers
Source code for this entry:
    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), NotEqual(Add(x, Mul(y, ConstI)), 0))))

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2021-03-15 19:12:00.328586 UTC