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Fungrim entry: e103e7

eiz=cos ⁣(z)+isin ⁣(z){e}^{i z} = \cos\!\left(z\right) + i \sin\!\left(z\right)
Assumptions:zCz \in \mathbb{C}
TeX:
{e}^{i z} = \cos\!\left(z\right) + i \sin\!\left(z\right)

z \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
Expez{e}^{z} Exponential function
ConstIii Imaginary unit
Sinsin ⁣(z)\sin\!\left(z\right) Sine
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("e103e7"),
    Formula(Equal(Exp(Mul(ConstI, z)), Add(Cos(z), Mul(ConstI, Sin(z))))),
    Variables(z),
    Assumptions(Element(z, CC)))

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

2019-08-21 11:44:15.926409 UTC