Issolvi {l}{x=frac{x_{1}x_{2}+y_{1}y_{2}}{x_2^2+y_2^2}}{y={(x_2^2+y_2^2)}}{z=y}{a=z}{b=a}{text{Solvefor}ctext{where}}{c=b}

$$\left. \begin{array} { l } { x = \frac{x_{1} x_{2} + y_{1} y_{2}}{x_{2} ^ {2} + y_{2} ^ {2}} }\\ { y = {(x_{2} ^ {2} + y_{2} ^ {2})} }\\ { z = y }\\ { a = z }\\ { b = a }\\ { \text{Solve for } c \text{ where} } \\ { c = b } \end{array} \right.$$

Solvi għal x, y, z (complex solution)

$$x=\frac{x_{1}x_{2}+y_{1}y_{2}}{x_{2}^{2}+y_{2}^{2}}$$

$$y=x_{2}^{2}+y_{2}^{2}$$

$$z=x_{2}^{2}+y_{2}^{2}$$

$$\left(x_{2}=-\sqrt{c-y_{2}^{2}}\text{ and }arg(iy_{2})\geq \pi \text{ and }y_{2}\neq 0\text{ and }arg(-iy_{2})\geq \pi \text{ and }a=c\text{ and }b=c\right)\text{ or }\left(x_{2}=-\sqrt{c-y_{2}^{2}}\text{ and }c\neq 0\text{ and }a=c\text{ and }b=c\right)\text{ or }\left(x_{2}=\sqrt{c-y_{2}^{2}}\text{ and }arg(iy_{2})\geq \pi \text{ and }y_{2}\neq 0\text{ and }arg(-iy_{2})\geq \pi \text{ and }a=c\text{ and }b=c\right)\text{ or }\left(x_{2}=\sqrt{c-y_{2}^{2}}\text{ and }c\neq 0\text{ and }a=c\text{ and }b=c\right)$$

Solvi għal x, y, z

$$x=\frac{x_{1}x_{2}+y_{1}y_{2}}{x_{2}^{2}+y_{2}^{2}}$$

$$y=x_{2}^{2}+y_{2}^{2}$$

$$z=x_{2}^{2}+y_{2}^{2}$$

$$b=c\text{ and }a=c\text{ and }\left(y_{2}\neq 0\text{ or }x_{2}\neq 0\right)\text{ and }\left(c>y_{2}^{2}\text{ or }y_{2}\neq 0\right)\text{ and }c\geq y_{2}^{2}\text{ and }|x_{2}|=\sqrt{c-y_{2}^{2}}$$