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Jee Main 2025 — Medium JEE math MCQ

If $\alpha$ and $\beta$ are the roots of the equation $2x^2 - 3x - 2i = 0$, where $i = \sqrt{-1}$, then $16 \cdot \text{Re} \left(\frac{\alpha^{19} + \beta^{19} + \alpha^{11} + \beta^{11}}{\alpha^{5} + \beta^{5}}\right) \cdot \text{Im} \left(\frac{\alpha^{19} + \beta^{19} + \alpha^{11} + \beta^{11}}{\alpha^{5} + \beta^{5}}\right)$ is equal to
  1. A. 441
  2. B. 398
  3. C. 312
  4. D. 409

Solution

The correct option is **A**. (A. 441)

MATH

medium • PYQ Reworded
Question
Read carefully, then pick the best option.
If α\alpha and β\beta are the roots of the equation 2x2−3x−2i=02x^2 - 3x - 2i = 0, where i=−1i = \sqrt{-1}, then 16⋅Re(α19+β19+α11+β11α5+β5)⋅Im(α19+β19+α11+β11α5+β5)16 \cdot \text{Re} \left(\frac{\alpha^{19} + \beta^{19} + \alpha^{11} + \beta^{11}}{\alpha^{5} + \beta^{5}}\right) \cdot \text{Im} \left(\frac{\alpha^{19} + \beta^{19} + \alpha^{11} + \beta^{11}}{\alpha^{5} + \beta^{5}}\right) is equal to
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