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Fungrim entry: a3a253

log ⁣(ez)=z2πiIm(z)2π12\log\!\left({e}^{z}\right) = z - 2 \pi i \left\lceil \frac{\operatorname{Im}(z)}{2 \pi} - \frac{1}{2} \right\rceil
Assumptions:zCz \in \mathbb{C}
\log\!\left({e}^{z}\right) = z - 2 \pi i \left\lceil \frac{\operatorname{Im}(z)}{2 \pi} - \frac{1}{2} \right\rceil

z \in \mathbb{C}
Fungrim symbol Notation Short description
Loglog(z)\log(z) Natural logarithm
Expez{e}^{z} Exponential function
Piπ\pi The constant pi (3.14...)
ConstIii Imaginary unit
ImIm(z)\operatorname{Im}(z) Imaginary part
CCC\mathbb{C} Complex numbers
Source code for this entry:
    Formula(Equal(Log(Exp(z)), Sub(z, Mul(Mul(Mul(2, Pi), ConstI), Ceil(Sub(Div(Im(z), Mul(2, Pi)), Div(1, 2))))))),
    Assumptions(Element(z, CC)))

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2021-03-15 19:12:00.328586 UTC