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Fungrim entry: caf706

sgn ⁣(ez)=exp ⁣(Im ⁣(z)i)\operatorname{sgn}\!\left({e}^{z}\right) = \exp\!\left(\operatorname{Im}\!\left(z\right) i\right)
Assumptions:zCz \in \mathbb{C}
TeX:
\operatorname{sgn}\!\left({e}^{z}\right) = \exp\!\left(\operatorname{Im}\!\left(z\right) i\right)

z \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
Signsgn ⁣(z)\operatorname{sgn}\!\left(z\right) Sign function
Expez{e}^{z} Exponential function
ImIm ⁣(z)\operatorname{Im}\!\left(z\right) Imaginary part
ConstIii Imaginary unit
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("caf706"),
    Formula(Equal(Sign(Exp(z)), Exp(Mul(Im(z), ConstI)))),
    Variables(z),
    Assumptions(Element(z, CC)))

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2019-08-21 11:44:15.926409 UTC