x^y=1 सोडवा

$$x ^ { y } = 1$$

x साठी सोडवा (जटिल उत्तर)

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

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

y साठी सोडवा (जटिल उत्तर)

$$\left\{\begin{matrix}y=\frac{2\pi n_{1}i}{\ln(x)}\text{, }n_{1}\in \mathrm{Z}\text{, }&x\neq 1\text{ and }x\neq 0\\y\in \mathrm{C}\text{, }&x=1\end{matrix}\right.$$

x साठी सोडवा

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

y साठी सोडवा

$$\left\{\begin{matrix}y=0\text{, }&x\neq 0\text{ and }|x|\neq 1\\y\in \mathrm{R}\text{, }&x=1\end{matrix}\right.$$