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Fungrim entry: b2a880

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

x \in \mathbb{R} \;\mathbin{\operatorname{and}}\; y \in \mathbb{R}
Definitions:
Fungrim symbol Notation Short description
Argarg⁡(z)\arg(z) Complex argument
ConstIii Imaginary unit
Atan2atan2⁡ ⁣(y,x)\operatorname{atan2}\!\left(y, x\right) Two-argument inverse tangent
RRR\mathbb{R} Real numbers
Source code for this entry:
Entry(ID("b2a880"),
    Formula(Equal(Arg(Add(x, Mul(y, ConstI))), Atan2(y, x))),
    Variables(x, y),
    Assumptions(And(Element(x, RR), Element(y, RR))))

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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