Atrisiniet -rv^r=1

$$- r v ^ { r } = 1$$

Atrast v (complex solution)

$$v=e^{-\frac{2\pi n_{1}iRe(r)}{\left(Re(r)\right)^{2}+\left(Im(r)\right)^{2}}-\frac{2\pi n_{1}Im(r)}{\left(Re(r)\right)^{2}+\left(Im(r)\right)^{2}}+\frac{arg(-\frac{1}{r})Im(r)+iarg(-\frac{1}{r})Re(r)}{\left(Re(r)\right)^{2}+\left(Im(r)\right)^{2}}}\left(|r|\right)^{\frac{-Re(r)+iIm(r)}{\left(Re(r)\right)^{2}+\left(Im(r)\right)^{2}}}$$

$$n_{1}\in \mathrm{Z}$$

$$r\neq 0$$

Atrast v

$$\left\{\begin{matrix}v=\left(-\frac{1}{r}\right)^{\frac{1}{r}}\text{, }&\left(Numerator(r)\text{bmod}2=1\text{ and }Denominator(r)\text{bmod}2=1\text{ and }r>0\right)\text{ or }\left(\left(-\frac{1}{r}\right)^{\frac{1}{r}}>0\text{ and }r<0\right)\text{ or }\left(\left(-\frac{1}{r}\right)^{\frac{1}{r}}<0\text{ and }Denominator(r)\text{bmod}2=1\text{ and }r<0\right)\\v=-\left(-\frac{1}{r}\right)^{\frac{1}{r}}\text{, }&\left(Numerator(r)\text{bmod}2=1\text{ and }r>0\text{ and }Numerator(r)\text{bmod}2=0\text{ and }Denominator(r)\text{bmod}2=1\right)\text{ or }\left(r<0\text{ and }\left(-\frac{1}{r}\right)^{\frac{1}{r}}<0\text{ and }Numerator(r)\text{bmod}2=0\right)\text{ or }\left(r<0\text{ and }\left(-\frac{1}{r}\right)^{\frac{1}{r}}>0\text{ and }Numerator(r)\text{bmod}2=0\text{ and }Denominator(r)\text{bmod}2=1\right)\end{matrix}\right,$$