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