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Fungrim entry: 1232f7

reiθ=reiθ/2\sqrt{r {e}^{i \theta}} = \sqrt{r} {e}^{i \theta / 2}
Assumptions:r[0,)andθ(π,π]r \in \left[0, \infty\right) \,\mathbin{\operatorname{and}}\, \theta \in \left(-\pi, \pi\right]
TeX:
\sqrt{r {e}^{i \theta}} = \sqrt{r} {e}^{i \theta / 2}

r \in \left[0, \infty\right) \,\mathbin{\operatorname{and}}\, \theta \in \left(-\pi, \pi\right]
Definitions:
Fungrim symbol Notation Short description
Sqrtz\sqrt{z} Principal square root
Expez{e}^{z} Exponential function
ConstIii Imaginary unit
ClosedOpenInterval[a,b)\left[a, b\right) Closed-open interval
Infinity\infty Positive infinity
OpenClosedInterval(a,b]\left(a, b\right] Open-closed interval
ConstPiπ\pi The constant pi (3.14...)
Source code for this entry:
Entry(ID("1232f7"),
    Formula(Equal(Sqrt(Mul(r, Exp(Mul(ConstI, theta)))), Mul(Sqrt(r), Exp(Div(Mul(ConstI, theta), 2))))),
    Variables(r, theta),
    Assumptions(And(Element(r, ClosedOpenInterval(0, Infinity)), Element(theta, OpenClosedInterval(Neg(ConstPi), ConstPi)))))

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

2019-08-21 11:44:15.926409 UTC