Let the product of ω₁ = (8 + i) sin θ + (7 + 4i) cos θ and ω₂ = (… | JEE Main 2025 Mathematics PYQ

MCQMediumJEE Main 2025 · 4 April, Shift 2Complex Numbers Basics

Let the product of $\omega_1 = (8 + i) \sin \theta + (7 + 4i) \cos \theta$ and $\omega_2 = (1 + 8i) \sin \theta + (4 + 7i) \cos \theta$ be $\alpha + i\beta$ , where $i = \sqrt{-1}$ . Let $p$ and $q$ be the maximum and the minimum values of $\alpha + \beta$ respectively. Then $p + q$ is equal to:

A
$140$
B
$130$
C
$160$
D
$150$

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