Solucionar z^n-1=n+10^n

$$z ^ { n - 1 } = n + 10 ^ { n }$$

Resolver para z (solución compleja)

$$z=\left(|n+10^{n}|\right)^{\frac{Re(n)-iIm(n)-1}{\left(Re(n)\right)^{2}+\left(Im(n)\right)^{2}-2Re(n)+1}}e^{\frac{Im(n)arg(n+10^{n})+iRe(n)arg(n+10^{n})-iarg(n+10^{n})}{\left(Re(n)\right)^{2}+\left(Im(n)\right)^{2}-2Re(n)+1}-\frac{2iRe(n)\pi n_{1}}{\left(Re(n)\right)^{2}+\left(Im(n)\right)^{2}-2Re(n)+1}-\frac{2\pi n_{1}Im(n)}{\left(Re(n)\right)^{2}+\left(Im(n)\right)^{2}-2Re(n)+1}+\frac{2i\pi n_{1}}{\left(Re(n)\right)^{2}+\left(Im(n)\right)^{2}-2Re(n)+1}}$$

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

Resolver para z

$$\left\{\begin{matrix}z=\left(n+10^{n}\right)^{\frac{1}{n-1}}\text{, }&\left(Numerator(n-1)\text{bmod}2=1\text{ and }n\neq 1\text{ and }Denominator(n)\text{bmod}2=1\text{ and }n+10^{n}<0\text{ and }\left(n+10^{n}\right)^{\frac{1}{n-1}}\neq 0\right)\text{ or }\left(n\neq 1\text{ and }n+10^{n}>0\right)\text{ or }\left(\left(n+10^{n}\right)^{\frac{1}{n-1}}<0\text{ and }n+10^{n}=0\text{ and }n>1\text{ and }Denominator(n)\text{bmod}2=1\right)\text{ or }\left(\left(n+10^{n}\right)^{\frac{1}{n-1}}=0\text{ and }Numerator(n-1)\text{bmod}2=1\text{ and }Denominator(n)\text{bmod}2=1\text{ and }n+10^{n}<0\text{ and }n>1\right)\text{ or }\left(n+10^{n}=0\text{ and }n>1\text{ and }\left(n+10^{n}\right)^{\frac{1}{n-1}}>0\right)\text{ or }\left(\left(n+10^{n}\right)^{\frac{1}{n-1}}=0\text{ and }n>1\text{ and }n+10^{n}\geq 0\right)\\z=-\left(n+10^{n}\right)^{\frac{1}{n-1}}\text{, }&\left(n+10^{n}<0\text{ and }Numerator(n-1)\text{bmod}2=1\text{ and }n\neq 1\text{ and }Numerator(n-1)\text{bmod}2=0\text{ and }Denominator(n)\text{bmod}2=1\text{ and }\left(n+10^{n}\right)^{\frac{1}{n-1}}\neq 0\right)\text{ or }\left(n+10^{n}=0\text{ and }n>1\text{ and }\left(n+10^{n}\right)^{\frac{1}{n-1}}>0\text{ and }Numerator(n-1)\text{bmod}2=0\text{ and }Denominator(n)\text{bmod}2=1\right)\text{ or }\left(n\neq 1\text{ and }n+10^{n}>0\text{ and }Numerator(n-1)\text{bmod}2=0\text{ and }Denominator(n)\text{bmod}2=1\right)\text{ or }\left(n+10^{n}<0\text{ and }Numerator(n-1)\text{bmod}2=1\text{ and }\left(n+10^{n}\right)^{\frac{1}{n-1}}=0\text{ and }Numerator(n-1)\text{bmod}2=0\text{ and }Denominator(n)\text{bmod}2=1\text{ and }n>1\right)\text{ or }\left(n+10^{n}=0\text{ and }n>1\text{ and }\left(n+10^{n}\right)^{\frac{1}{n-1}}<0\text{ and }Numerator(n-1)\text{bmod}2=0\right)\text{ or }\left(n+10^{n}>0\text{ and }n\neq 1\text{ and }\left(n+10^{n}\right)^{\frac{1}{n-1}}<0\text{ and }Numerator(n-1)\text{bmod}2=0\right)\text{ or }\left(\left(n+10^{n}\right)^{\frac{1}{n-1}}=0\text{ and }Numerator(n-1)\text{bmod}2=0\text{ and }n>1\text{ and }n+10^{n}\geq 0\right)\end{matrix}\right,$$