JEE Mains · Maths · STD 11 - 4.1 complex nubers
Let the product of \(\omega_1=(8+i) \sin \theta+(7+4 i) \cos \theta\) and \(\omega_2=(1+8 i) \sin \theta+(4+7 i) \cos \theta\) be \(\alpha+i \beta\), \(\mathrm{i}=\sqrt{-1}\). Let p and q be the maximum and the minimum values of \(\alpha+\beta\) respectively.
- A \(140\)
- B \(130\)
- C \(160\)
- D \(150\)
Answer & Solution
Correct Answer
(B) \(130\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \omega_1=(8 \sin \theta+7 \cos \theta)+i(\sin \theta+4 \cos \theta) \\ & \omega_2=(\sin \theta+4 \cos \theta)+i(8 \sin \theta+7 \cos \theta) \\ & \omega_1 \omega_2=8 \sin ^2 \theta+7 \sin \theta \cos \theta+32 \sin \theta \cos \theta+ \\ & 28 \cos ^2 \theta-8…
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