Fungrim home page

Fungrim entry: 15f92d

iz=cos ⁣(π2z)+sin ⁣(π2z)i{i}^{z} = \cos\!\left(\frac{\pi}{2} z\right) + \sin\!\left(\frac{\pi}{2} z\right) i
Assumptions:zCz \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
Powab{a}^{b} Power
ConstIii Imaginary unit
Coscos(z)\cos(z) Cosine
Piπ\pi The constant pi (3.14...)
Sinsin(z)\sin(z) Sine
CCC\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

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