Solve for P (complex solution)
\left\{\begin{matrix}P=\frac{\left(\frac{S}{r}\right)^{2}}{Q}\text{, }&S\neq 0\text{ and }r\neq 0\text{ and }Q\neq 0\text{ and }|arg(\sqrt{\frac{S^{2}}{r^{2}}}r)-arg(S)|<\pi \\P\neq 0\text{, }&Q\neq 0\text{ and }r=0\text{ and }S=0\end{matrix}\right.
Solve for Q (complex solution)
\left\{\begin{matrix}Q=\frac{\left(\frac{S}{r}\right)^{2}}{P}\text{, }&S\neq 0\text{ and }r\neq 0\text{ and }P\neq 0\text{ and }|arg(\sqrt{\frac{S^{2}}{r^{2}}}r)-arg(S)|<\pi \\Q\neq 0\text{, }&P\neq 0\text{ and }r=0\text{ and }S=0\end{matrix}\right.
Solve for P
\left\{\begin{matrix}P=\frac{\left(\frac{S}{r}\right)^{2}}{Q}\text{, }&\left(Q\neq 0\text{ and }r<0\text{ and }S<0\right)\text{ or }\left(Q\neq 0\text{ and }r>0\text{ and }S>0\right)\\P>0\text{, }&Q>0\text{ and }r=0\text{ and }S=0\\P<0\text{, }&Q<0\text{ and }r=0\text{ and }S=0\end{matrix}\right.
Solve for Q
\left\{\begin{matrix}Q=\frac{\left(\frac{S}{r}\right)^{2}}{P}\text{, }&\left(P\neq 0\text{ and }r<0\text{ and }S<0\right)\text{ or }\left(P\neq 0\text{ and }r>0\text{ and }S>0\right)\\Q<0\text{, }&P<0\text{ and }r=0\text{ and }S=0\\Q>0\text{, }&P>0\text{ and }r=0\text{ and }S=0\end{matrix}\right.
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