1.
If α\alpha and β\beta are the roots of the equation 2z23z2i=02z^2 - 3z - 2i = 0, where i=1i = \sqrt{-1}, then Re ⁣(α19+β19+α11+β11α15+β15)\mathrm{Re}\!\left(\dfrac{\alpha^{19} + \beta^{19} + \alpha^{11} + \beta^{11}}{\alpha^{15} + \beta^{15}}\right) is equal to: