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Fungrim entry: e722ca

Im⁡ ⁣(z)=sgn⁡ ⁣(Im⁡ ⁣(z))∣z∣−Re⁡ ⁣(z)2\operatorname{Im}\!\left(\sqrt{z}\right) = \operatorname{sgn}\!\left(\operatorname{Im}\!\left(z\right)\right) \sqrt{\frac{\left|z\right| - \operatorname{Re}\!\left(z\right)}{2}}
Assumptions:z∈Cz \in \mathbb{C}
TeX:
\operatorname{Im}\!\left(\sqrt{z}\right) = \operatorname{sgn}\!\left(\operatorname{Im}\!\left(z\right)\right) \sqrt{\frac{\left|z\right| - \operatorname{Re}\!\left(z\right)}{2}}

z \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
ImIm⁡ ⁣(z)\operatorname{Im}\!\left(z\right) Imaginary part
Sqrtz\sqrt{z} Principal square root
Signsgn⁡ ⁣(z)\operatorname{sgn}\!\left(z\right) Sign function
Abs∣z∣\left|z\right| Absolute value
ReRe⁡ ⁣(z)\operatorname{Re}\!\left(z\right) Real part
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("e722ca"),
    Formula(Equal(Im(Sqrt(z)), Mul(Sign(Im(z)), Sqrt(Div(Sub(Abs(z), Re(z)), 2))))),
    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.

2019-06-18 07:49:59.356594 UTC