Solve S^2=P^2+Q_L^2

$$S ^ { 2 } = P ^ { 2 } + Q _ { L } ^ { 2 }$$

Solve for P (complex solution)

$$P=-\sqrt{S^{2}-Q_{L}^{2}}$$

$$P=\sqrt{S^{2}-Q_{L}^{2}}$$

Solve for Q_L (complex solution)

$$Q_{L}=-\sqrt{S^{2}-P^{2}}$$

$$Q_{L}=\sqrt{S^{2}-P^{2}}$$

Solve for P

$$P=\sqrt{S^{2}-Q_{L}^{2}}$$

$$P=-\sqrt{S^{2}-Q_{L}^{2}}\text{, }|S|\geq |Q_{L}|$$

Solve for Q_L

$$Q_{L}=\sqrt{S^{2}-P^{2}}$$

$$Q_{L}=-\sqrt{S^{2}-P^{2}}\text{, }|S|\geq |P|$$