Explanation

(c)
Let $x = \sqrt{- 1 - \sqrt{- 1 - \sqrt{- 1 - ...\infty}}}$
Then, $x = \sqrt{- 1 - x}\ \ or\ x^{2} = - 1 - x$
or $x^{2} + x + 1 = 0$
$\therefore\ \ x = \frac{- 1 \pm \sqrt{1 - 4.1.1}}{2.1} = \frac{- 1 \pm \sqrt{- 3}}{2}$
$= \ \frac{- 1 \pm \sqrt{3}i}{2} = \omega\ \ or\ \omega^{2}$