Explanation

(b)
$\frac{\left\lbrack \left( \cos{20{^\circ}} + i\sin{20{^\circ}} \right)\left( \cos{75{^\circ} + i\sin{75{^\circ}}} \right)(\cos{10{^\circ} + i\sin{10{^\circ}}}) \right\rbrack}{\sin{15{^\circ} - i\cos{15{^\circ}}}}$
$= \frac{e^{i20{^\circ}}e^{i75{^\circ}}.e^{i10{^\circ}}}{- i(\cos{15{^\circ} + i\sin{15{^\circ}}})}$
$= - \frac{e^{i105{^\circ}}}{ie^{i15{^\circ}}}$
$= - \frac{e^{i90{^\circ}}}{i} = - 1$