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Complex Numbers question

2025 · 24 Jan · Shift 1 · Q32

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PYQ Library
JEE Main
Mathematics
Complex Numbers
2025 · 24 Jan · Shift 1 · Q32

Complex Numbers question

2025 · 24 Jan · Shift 1 · Q32

JEE MainMathematicsComplex NumbersMCQ+4 / −1

If

\alpha

and

\beta

are the roots of the equation

2 z^2-3 z-2 i=0

, where

i=\sqrt{-1}

, then

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

is equal to

A
441
B
312
C
409
D
398

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