Question

Find imaginary part of $\sin^{- 1}\left( \frac{5\sqrt{7} - 9i}{16} \right)$

• A. $\log 2$
• B. $- \log 2$
• C. 0
• D. None of these

Answer 1

Answer: (B)

$- \log 2$

Answer 2

$\left\lbrack \sin^{- 1}\left( \frac{5\sqrt{7}}{16} - \frac{9i}{16} \right) \right\rbrack = - \log\left\lbrack \sqrt{\frac{9}{16}} + \sqrt{1 + \frac{9}{16}} \right\rbrack$=$- \log(2)$