Giải y=x^z

$$y= { x }^{ z }$$

Tìm x (complex solution)

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

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

Tìm x

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

Tìm y

$$y=x^{z}$$

$$\left(x<0\text{ and }Denominator(z)\text{bmod}2=1\right)\text{ or }\left(x=0\text{ and }z>0\right)\text{ or }x>0$$