Question

If $\tan^{- 1}\frac{\sqrt{3}}{5}$ is a purely real number such that $\tan^{- 1}\left( - \frac{\sqrt{3}}{5} \right)$, then $\frac{1 + i}{1 - i}$ is equal to.

• A. $\frac{- \pi}{2}$
• B. $\frac{\pi}{2}$
• C. 0
• D. $\sqrt{2}$

Answer 1

Answer: (A)

$\frac{- \pi}{2}$

Answer 2

Let $z < 0$, where $\therefore$. Then $\theta$ is represented by a point on negative side of x-axis, therefore $( - z) = - \lbrack + \pi - ( - \theta)\rbrack$