WBJEE · Maths · Complex Number
If \(|z-25 i| \leq 15\), then Maximum \(\arg (z)-\) Minimum \(\arg (z)\) is equal to
- A \(2 \cos ^{-1}\left(\frac{3}{5}\right)\)
- B \(2 \cos ^{-1}\left(\frac{4}{5}\right)\)
- C \(\frac{\pi}{2}+\cos ^{-1}\left(\frac{3}{5}\right)\)
- D \(\sin ^{-1}\left(\frac{3}{5}\right)-\cos ^{-1}\left(\frac{3}{5}\right)\)
Answer & Solution
Correct Answer
(B) \(2 \cos ^{-1}\left(\frac{4}{5}\right)\)
Step-by-step Solution
Detailed explanation
\[ \because \cos \theta=\frac{15}{25}=\frac{3}{5} \] \(\therefore \operatorname{Min} \arg (z)=\cos ^{-1}\left(\frac{3}{5}\right)\) \(\operatorname{Max} \arg (z)=\pi-\cos ^{-1}\left(\frac{3}{5}\right)=\frac{\pi}{2}+\sin ^{-1}\left(\frac{3}{5}\right)\) \(\therefore\) difference…
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