다음을 풀어보세요: y^x=1

$$y ^ { x } = 1$$

x에 대한 해 (complex solution)

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

y에 대한 해 (complex solution)

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

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

x에 대한 해

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

y에 대한 해

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