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Fungrim entry: a0d93c

arg ⁣(ez)=Im(z)\arg\!\left({e}^{z}\right) = \operatorname{Im}(z)
Assumptions:zCandIm(z)(π,π]z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \operatorname{Im}(z) \in \left(-\pi, \pi\right]
TeX:
\arg\!\left({e}^{z}\right) = \operatorname{Im}(z)

z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \operatorname{Im}(z) \in \left(-\pi, \pi\right]
Definitions:
Fungrim symbol Notation Short description
Argarg(z)\arg(z) Complex argument
Expez{e}^{z} Exponential function
ImIm(z)\operatorname{Im}(z) Imaginary part
CCC\mathbb{C} Complex numbers
OpenClosedInterval(a,b]\left(a, b\right] Open-closed interval
ConstPiπ\pi The constant pi (3.14...)
Source code for this entry:
Entry(ID("a0d93c"),
    Formula(Equal(Arg(Exp(z)), Im(z))),
    Variables(z),
    Assumptions(And(Element(z, CC), Element(Im(z), OpenClosedInterval(Neg(ConstPi), ConstPi)))))

Topics using this entry

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

2019-10-05 13:11:19.856591 UTC