Fungrim entry: 77d6bf

{e}^{a + b i} = {e}^{a} \left(\cos(b) + \sin(b) i\right)

Assumptions:

a \in \mathbb{C} \;\mathbin{\operatorname{and}}\; b \in \mathbb{C}

TeX:

{e}^{a + b i} = {e}^{a} \left(\cos(b) + \sin(b) i\right)

a \in \mathbb{C} \;\mathbin{\operatorname{and}}\; b \in \mathbb{C}

Definitions:

Fungrim symbol	Notation	Short description
`Exp`	${e}^{z}$	Exponential function
`ConstI`	$i$	Imaginary unit
`Cos`	$\cos(z)$	Cosine
`Sin`	$\sin(z)$	Sine
`CC`	$\mathbb{C}$	Complex numbers

Source code for this entry:

Entry(ID("77d6bf"),
    Formula(Equal(Exp(Add(a, Mul(b, ConstI))), Mul(Exp(a), Add(Cos(b), Mul(Sin(b), ConstI))))),
    Variables(a, b),
    Assumptions(And(Element(a, CC), Element(b, 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.

2021-03-15 19:12:00.328586 UTC