सोडोवचें x^n=-1

$$x ^ { n } = - 1$$

n खातीर सोडोवचें (जटील सोल्यूशन)

$$n=\frac{2\pi n_{1}i}{\ln(x)}+\frac{\pi i}{\ln(x)}$$

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

$$x\neq 1\text{ and }x\neq 0$$

x खातीर सोडोवचें (जटील सोल्यूशन)

$$x=e^{-\frac{2\pi n_{1}iRe(n)}{\left(Re(n)\right)^{2}+\left(Im(n)\right)^{2}}-\frac{2\pi n_{1}Im(n)}{\left(Re(n)\right)^{2}+\left(Im(n)\right)^{2}}+\frac{\pi \left(Im(n)+iRe(n)\right)}{\left(Re(n)\right)^{2}+\left(Im(n)\right)^{2}}}$$

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

n खातीर सोडोवचें

$$n\in \mathrm{R}$$

$$x=-1\text{ and }Denominator(n)\text{bmod}2=1\text{ and }Numerator(n)\text{bmod}2=1$$

x खातीर सोडोवचें

$$\left\{\begin{matrix}x=-1\text{, }&Numerator(n)\text{bmod}2=1\text{ and }Denominator(n)\text{bmod}2=1\\x=1\text{, }&Numerator(n)\text{bmod}2=1\text{ and }Denominator(n)\text{bmod}2=1\text{ and }Numerator(n)\text{bmod}2=0\end{matrix}\right.$$