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WBJEE · Maths · Complex Number

If \(|z-25 i| \leq 15\), then Maximum \(\arg (z)-\) Minimum \(\arg (z)\) is equal to

  1. A \(2 \cos ^{-1}\left(\frac{3}{5}\right)\)
  2. B \(2 \cos ^{-1}\left(\frac{4}{5}\right)\)
  3. C \(\frac{\pi}{2}+\cos ^{-1}\left(\frac{3}{5}\right)\)
  4. D \(\sin ^{-1}\left(\frac{3}{5}\right)-\cos ^{-1}\left(\frac{3}{5}\right)\)
Verified Solution

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…