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Fungrim entry: 97ba8d

ez+nπi=(1)nez{e}^{z + n \pi i} = {\left(-1\right)}^{n} {e}^{z}
Assumptions:zC  and  nZz \in \mathbb{C} \;\mathbin{\operatorname{and}}\; n \in \mathbb{Z}
TeX:
{e}^{z + n \pi i} = {\left(-1\right)}^{n} {e}^{z}

z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; n \in \mathbb{Z}
Definitions:
Fungrim symbol Notation Short description
Expez{e}^{z} Exponential function
Piπ\pi The constant pi (3.14...)
ConstIii Imaginary unit
Powab{a}^{b} Power
CCC\mathbb{C} Complex numbers
ZZZ\mathbb{Z} Integers
Source code for this entry:
Entry(ID("97ba8d"),
    Formula(Equal(Exp(Add(z, Mul(Mul(n, Pi), ConstI))), Mul(Pow(-1, n), Exp(z)))),
    Variables(z, n),
    Assumptions(And(Element(z, CC), Element(n, ZZ))))

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

2020-04-08 16:14:44.404316 UTC