JEE Main 2025 (Online) 4th April Evening ShiftQuestion 1
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 $\alpha+i\beta$, $i=\sqrt{-1}$. Let $p$ and $q$ be the maximum and the minimum values of $\alpha+\beta$ respectively. Then $p+q$ is equal to :
Complex Numbers
Solution
Expanding, $\alpha+\beta=\operatorname{Re}+\operatorname{Im}$ of $\omega_1\omega_2$ simplifies to $65+60\sin2\theta$. So $p=125$, $q=5$, $p+q=130$. Option (A).