$a=\frac{-1111820911i}{rtk^{2}}$
$k\neq 0\text{ and }t\neq 0\text{ and }r\neq 0$

$k=\sqrt{2223641822}\left(-\frac{1}{2}+\frac{1}{2}i\right)a^{-\frac{1}{2}}r^{-\frac{1}{2}}t^{-\frac{1}{2}}$
$k=\sqrt{2223641822}\left(\frac{1}{2}-\frac{1}{2}i\right)a^{-\frac{1}{2}}r^{-\frac{1}{2}}t^{-\frac{1}{2}}\text{, }t\neq 0\text{ and }r\neq 0\text{ and }a\neq 0$