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Fungrim entry: e722ca

Im ⁣(z)=sgn ⁣(Im(z))zRe(z)2\operatorname{Im}\!\left(\sqrt{z}\right) = \operatorname{sgn}\!\left(\operatorname{Im}(z)\right) \sqrt{\frac{\left|z\right| - \operatorname{Re}(z)}{2}}
Assumptions:zCz \in \mathbb{C}
TeX:
\operatorname{Im}\!\left(\sqrt{z}\right) = \operatorname{sgn}\!\left(\operatorname{Im}(z)\right) \sqrt{\frac{\left|z\right| - \operatorname{Re}(z)}{2}}

z \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
ImIm(z)\operatorname{Im}(z) Imaginary part
Sqrtz\sqrt{z} Principal square root
Signsgn(z)\operatorname{sgn}(z) Sign function
Absz\left|z\right| Absolute value
ReRe(z)\operatorname{Re}(z) 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)))

Topics using this entry

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

2019-11-19 15:10:20.037976 UTC