Fungrim entry: 15f92d

{i}^{z} = \cos\!\left(\frac{\pi}{2} z\right) + \sin\!\left(\frac{\pi}{2} z\right) i

Assumptions:

z \in \mathbb{C}

TeX:

{i}^{z} = \cos\!\left(\frac{\pi}{2} z\right) + \sin\!\left(\frac{\pi}{2} z\right) i

z \in \mathbb{C}

Definitions:

Fungrim symbol	Notation	Short description
`Pow`	${a}^{b}$	Power
`ConstI`	$i$	Imaginary unit
`Cos`	$\cos(z)$	Cosine
`Pi`	$\pi$	The constant pi (3.14...)
`Sin`	$\sin(z)$	Sine
`CC`	$\mathbb{C}$	Complex numbers

Source code for this entry:

Entry(ID("15f92d"),
    Formula(Equal(Pow(ConstI, z), Add(Cos(Mul(Div(Pi, 2), z)), Mul(Sin(Mul(Div(Pi, 2), z)), ConstI)))),
    Variables(z),
    Assumptions(Element(z, CC)))

Topics using this entry

Imaginary unit

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