If \alpha and \beta are the roots of the equation 2 z^2-3 z-2 i= \text{ 0, where } i=\sqrt{-1}, \text{ then } \text{ 16 } \cdot {\Re} ( {\alpha^{19}+\beta^{19}+\alpha^{11}+\beta^{11}}/{\alpha^{15}+\beta^{15}}) \cdot {\lm} ( {\alpha^{19}+\beta^{19}+\alpha^{11}+\beta^{11}}/{\alpha^{15}+\beta^{15}}) is equal to [24 Jan 2025 Shift 1]

JEE Main 24 Jan 2025 Shift 1 Paper

Section: Mathematics

Question : 15 of 75

Marks: +1, -0

If α and β are the roots of the equation 2z2−3z−2i= ‌‌ 0, where ‌‌‌i=√−1,‌‌‌ then ‌
‌‌ 16 ‌⋅Re(‌

α19+β19+α11+β11

α15+β15

)⋅lm(‌

α19+β19+α11+β11

α15+β15

)
is equal to

[24 Jan 2025 Shift 1]

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