Explanation

(c)
Let $z = \left( \frac{1 + i}{\sqrt{2}} \right)^{2/3} = \left( \frac{1}{\sqrt{2}} + \frac{i}{\sqrt{2}} \right)^{2/3}$
$= \left( \cos{\frac{\pi}{4} + i\sin\frac{\pi}{4}} \right)^{2/3}$
$= e^{\left( \frac{i\pi}{4} \right)^{2/3}} = e^{i\pi/6}$
$= \cos{(2n + 1)\frac{\pi}{6} + i\sin{(2n + 1)\frac{\pi}{6}\ }}$
Put $n = 1$,
$z = \cos{\left( \frac{3\pi}{6} \right) + i\sin\left( \frac{3\pi}{6} \right) = 0 + i = i}$