Let S ={z ∈ C -{i, 2 i}: (z^2+8 i z-15)/(z^2-3 i z-2) ∈ R }. If α-13/11 i ∈ S, α ∈ R -{0}, then 242 α^2 is equal to ____.

Let $\displaystyle \mathrm{S}=\left\{z \in \mathbb{C}-\{i, 2 i\}: \frac{z^2+8 i z-15}{z^2-3 i z-2} \in \mathbb{R}\right\}$. If $\displaystyle \alpha-\frac{13}{11} i \in \mathrm{~S}, \alpha \in \mathbb{R}-\{0\}$, then $\displaystyle 242 \alpha^2$ is equal to $\displaystyle \_\_\_\_$.