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Fungrim entry: 099b19

Re⁡ ⁣(log⁡(z))=log⁡ ⁣(∣z∣)\operatorname{Re}\!\left(\log(z)\right) = \log\!\left(\left|z\right|\right)
Assumptions:z∈C∖{0}z \in \mathbb{C} \setminus \left\{0\right\}
TeX:
\operatorname{Re}\!\left(\log(z)\right) = \log\!\left(\left|z\right|\right)

z \in \mathbb{C} \setminus \left\{0\right\}
Definitions:
Fungrim symbol Notation Short description
ReRe⁡(z)\operatorname{Re}(z) Real part
Loglog⁡(z)\log(z) Natural logarithm
Abs∣z∣\left|z\right| Absolute value
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("099b19"),
    Formula(Equal(Re(Log(z)), Log(Abs(z)))),
    Variables(z),
    Assumptions(Element(z, SetMinus(CC, Set(0)))))

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2021-03-15 19:12:00.328586 UTC