Explanation

(d)
$\because\ \ \ \ z = \frac{7 - i}{3 - 4i} = \frac{(7 - i)(3 + 4i)}{(3)^{2} - (4i)^{2}} = (1 + i)$
$\therefore\ \ \ z^{14} = (1 + i)^{14} = \left\lbrack \sqrt{2}\left( \cos{\frac{\pi}{4} + i\sin\frac{\pi}{4}} \right) \right\rbrack^{14}$
$= 2^{7}\left( \cos{\frac{7\pi}{2} + i\sin\frac{7\pi}{2}} \right) = - 2^{7}i$