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Fungrim entry: 13895b

log ⁣(z)=log ⁣(z)\log\!\left(\overline{z}\right) = \overline{\log\!\left(z\right)}
Assumptions:zC(,0]z \in \mathbb{C} \setminus \left(-\infty, 0\right]
TeX:
\log\!\left(\overline{z}\right) = \overline{\log\!\left(z\right)}

z \in \mathbb{C} \setminus \left(-\infty, 0\right]
Definitions:
Fungrim symbol Notation Short description
Loglog ⁣(z)\log\!\left(z\right) Natural logarithm
Conjugatez\overline{z} Complex conjugate
CCC\mathbb{C} Complex numbers
OpenClosedInterval(a,b]\left(a, b\right] Open-closed interval
Infinity\infty Positive infinity
Source code for this entry:
Entry(ID("13895b"),
    Formula(Equal(Log(Conjugate(z)), Conjugate(Log(z)))),
    Variables(z),
    Assumptions(Element(z, SetMinus(CC, OpenClosedInterval(Neg(Infinity), 0)))))

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

2019-09-15 11:00:55.020619 UTC