If α and β are the roots of the equation 2 z^2-3 z-2 i=0, where i=√ -1, then 16 · Re ((α^19+β^19+α^11+β^11)/(α^15+β^15)) · Im…

If $\displaystyle \alpha$ and $\displaystyle \beta$ are the roots of the equation $\displaystyle 2 z^2-3 z-2 i=0$, where $\displaystyle i=\sqrt{-1}$, then $\displaystyle 16 \cdot \operatorname{Re}\left(\frac{\alpha^{19}+\beta^{19}+\alpha^{11}+\beta^{11}}{\alpha^{15}+\beta^{15}}\right) \cdot \operatorname{Im}\left(\frac{\alpha^{19}+\beta^{19}+\alpha^{11}+\beta^{11}}{\alpha^{15}+\beta^{15}}\right)$ is equal to