Let the product of ω₁ = (8+i) sin θ + (7+4i) cos θ and ω₂ = (1+8i) sin θ + (4+7i) cos θ be α + iβ, where i=√(-1). Let p and q be the maximum and minimum values of α+β, respectively. Then p+q is equal to:

Complex Numbers and Quadratic Equations: JEE Main 2025 Mathematics question

JEE Main 2025 · April, Unspecified (session-level dataset) · Q105

JEE Main 2025April, Unspecified (session-level dataset)MathematicsMediumComplex Numbers and Quadratic Equations264× since 2002

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

\alpha + i\beta

, where

i=\sqrt{-1}

. Let

p

and

q

be the maximum and minimum values of

\alpha+\beta

, respectively. Then

p+q

is equal to: