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Fungrim entry: e2fac7

Im ⁣(ez)=eRe(z)sin ⁣(Im(z))\operatorname{Im}\!\left({e}^{z}\right) = {e}^{\operatorname{Re}(z)} \sin\!\left(\operatorname{Im}(z)\right)
Assumptions:zCz \in \mathbb{C}
TeX:
\operatorname{Im}\!\left({e}^{z}\right) = {e}^{\operatorname{Re}(z)} \sin\!\left(\operatorname{Im}(z)\right)

z \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
ImIm(z)\operatorname{Im}(z) Imaginary part
Expez{e}^{z} Exponential function
ReRe(z)\operatorname{Re}(z) Real part
Sinsin(z)\sin(z) Sine
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("e2fac7"),
    Formula(Equal(Im(Exp(z)), Mul(Exp(Re(z)), Sin(Im(z))))),
    Variables(z),
    Assumptions(Element(z, CC)))

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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2020-04-08 16:14:44.404316 UTC