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Previous Year Question (PYQs)
1
If $\alpha$ and $\beta$ are the roots of the equation $2x^2 - 3x - 2i = 0$, where $i = \sqrt{-1}$, then
$16 \cdot \text{Re}\left( \dfrac{\alpha^{19} + \beta^{19} + \alpha^{11} + \beta^{11}}{\alpha^5 + \beta^5} \right) \cdot \text{Im}\left( \dfrac{\alpha^{19} + \beta^{19} + \alpha^{11} + \beta^{11}}{\alpha^5 + \beta^5} \right)$
is equal to
Solution
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