Question

$$F=k\frac{Q1Q2}{P^{2}}$$

Solve for P (complex solution)

$\left\{\begin{matrix}P=-F^{-\frac{1}{2}}\sqrt{Q_{1}}\sqrt{Q_{2}}\sqrt{k}\text{; }P=F^{-\frac{1}{2}}\sqrt{Q_{1}}\sqrt{Q_{2}}\sqrt{k}\text{, }&Q_{2}\neq 0\text{ and }Q_{1}\neq 0\text{ and }k\neq 0\text{ and }F\neq 0\\P\neq 0\text{, }&\left(Q_{2}=0\text{ or }Q_{1}=0\text{ or }k=0\right)\text{ and }F=0\end{matrix}\right.$

Solve for F

$F=\frac{Q_{1}Q_{2}k}{P^{2}}$
$P\neq 0$