Fungrim entry: e2fac7

\operatorname{Im}\!\left({e}^{z}\right) = \exp\!\left(\operatorname{Re}\!\left(z\right)\right) \sin\!\left(\operatorname{Im}\!\left(z\right)\right)

Assumptions:

z \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
`Im`	$\operatorname{Im}\!\left(z\right)$	Imaginary part
`Exp`	${e}^{z}$	Exponential function
`Re`	$\operatorname{Re}\!\left(z\right)$	Real part
`Sin`	$\sin\!\left(z\right)$	Sine
`CC`	$\mathbb{C}$	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

Exponential function

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

2019-06-18 07:49:59.356594 UTC