Question

If | z – 25i | ≤ 15, then | maximum arg (z) – minimum arg (z) | equals –

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

Answer 1

Answer: (C)

$2\cos^{- 1}\left( \frac{4}{5} \right)$

Answer 2

Sol.

min arg (z) = q = cos^–1$\left( \frac{15}{25} \right)$= cos^–1 $\left( \frac{3}{5} \right)$

max arg (z) = p – q = p – cos^–1$\left( \frac{3}{5} \right)$

| max arg z – min arg z | = | p – 2q |

= | p – 2 cos^–1$\left( \frac{3}{5} \right)$|