$\left\{\begin{matrix}x=\frac{a^{2}+b^{2}}{2}\text{, }y=ab\text{; }x=\frac{a^{2}+b^{2}}{2}\text{, }y=-ab\text{, }&\left(arg(b^{2})<\pi \text{ and }arg(b)<\pi \text{ and }b\neq 0\text{ and }a=0\right)\text{ or }\left(\text{Indeterminate}\geq \pi \text{ and }b=0\text{ and }a=0\right)\text{ or }\left(arg(\left(b-a\right)\left(a+b\right))<\pi \text{ and }arg(b)<\pi \text{ and }b\neq 0\text{ and }arg(a)<\pi \text{ and }a\neq 0\right)\text{ or }\left(arg(a^{2})\geq \pi \text{ and }b=0\text{ and }arg(a)<\pi \text{ and }a\neq 0\right)\\x=\frac{a^{2}+b^{2}}{2}\text{, }y=\frac{-a^{2}-b^{2}}{2}\text{; }x=\frac{a^{2}+b^{2}}{2}\text{, }y=\frac{a^{2}+b^{2}}{2}\text{, }&\left(a=0\text{ and }b=0\right)\text{ or }\left(b=a\text{ and }arg(a)<\pi \text{ and }a\neq 0\right)\end{matrix}\right.$