Solve for y (complex solution)
\left\{\begin{matrix}y=-i\left(z-1\right)^{-\frac{1}{2}}\sqrt{2x}\sqrt{-z-1}\text{; }y=i\left(z-1\right)^{-\frac{1}{2}}\sqrt{2x}\sqrt{-z-1}\text{, }&x\neq 0\text{ and }z\neq 1\\y\neq 0\text{, }&x=0\text{ and }z=1\end{matrix}\right.
Solve for x
\left\{\begin{matrix}x=\frac{\left(z-1\right)y^{2}}{2\left(z+1\right)}\text{, }&y\neq 0\text{ and }z\neq -1\\x\neq 0\text{, }&y=0\text{ and }z=-1\end{matrix}\right.
Solve for y
\left\{\begin{matrix}y=\sqrt{\frac{2x\left(z+1\right)}{z-1}}\text{; }y=-\sqrt{\frac{2x\left(z+1\right)}{z-1}}\text{, }&\left(x>0\text{ and }z\leq -1\right)\text{ or }\left(z>1\text{ and }x>0\right)\text{ or }\left(z\geq -1\text{ and }z<1\text{ and }x<0\right)\\y\neq 0\text{, }&x=0\text{ and }z=1\end{matrix}\right.
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