If α and β are the roots of the equation 2x² - 3x - 2i = 0, where i = √(-1), then 16 · Re((α¹⁸ + β¹⁸ + α¹³ + β¹¹)/(α¹⁵ + β¹⁵)) · Im((α¹⁸ + β¹⁹ + α¹¹ + β¹¹)/(α¹⁵ + β¹⁵)) is equal to

Complex Numbers and Quadratic Equations: JEE Main 2025 Mathematics question

JEE Main 2025 · January, Unspecified (session-level dataset) · Q59

JEE Main 2025January, Unspecified (session-level dataset)MathematicsMediumComplex Numbers and Quadratic Equations264× since 2002

\alpha

and

\beta

are the roots of the equation

2x^2 - 3x - 2i = 0

, where

i = \sqrt{-1}

, then

16 \cdot \operatorname{Re}\left(\frac{\alpha^{18} + \beta^{18} + \alpha^{13} + \beta^{11}}{\alpha^{15} + \beta^{15}}\right) \cdot \operatorname{Im}\left(\frac{\alpha^{18} + \beta^{19} + \alpha^{11} + \beta^{11}}{\alpha^{15} + \beta^{15}}\right)

is equal to