Fungrim entry: b7d62b

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

Assumptions:

z \in \mathbb{C}

TeX:

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

z \in \mathbb{C}

Definitions:

Fungrim symbol	Notation	Short description
`Re`	$\operatorname{Re}\!\left(z\right)$	Real part
`Exp`	${e}^{z}$	Exponential function
`Im`	$\operatorname{Im}\!\left(z\right)$	Imaginary part
`CC`	$\mathbb{C}$	Complex numbers

Source code for this entry:

Entry(ID("b7d62b"),
    Formula(Equal(Re(Exp(z)), Mul(Exp(Re(z)), Cos(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