# Fungrim entry: 1232f7

$\sqrt{r {e}^{i \theta}} = \sqrt{r} {e}^{i \theta / 2}$
Assumptions:$r \in \left[0, \infty\right) \,\mathbin{\operatorname{and}}\, \theta \in \left(-\pi, \pi\right]$
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
Sqrt$\sqrt{z}$ Principal square root
Exp${e}^{z}$ Exponential function
ConstI$i$ Imaginary unit
ClosedOpenInterval$\left[a, b\right)$ Closed-open interval
Infinity$\infty$ Positive infinity
OpenClosedInterval$\left(a, b\right]$ Open-closed interval
ConstPi$\pi$ 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)))))

## Topics using this entry

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