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Fungrim entry: e2fac7

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

z \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
ImIm ⁣(z)\operatorname{Im}\!\left(z\right) Imaginary part
Expez{e}^{z} Exponential function
ReRe ⁣(z)\operatorname{Re}\!\left(z\right) Real part
Sinsin ⁣(z)\sin\!\left(z\right) 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)))

Topics using this entry

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

2019-08-21 11:44:15.926409 UTC