Помоги решить 5 задание

Решите задачу:

$1-\frac{\sqrt{3}}{2}+\frac{1}{2}i=1-\cos 30^{\circ}+\sin 30^{\circ}i= 2\sin^2 15^{\circ}+2\sin 15^{\circ}\cos 15^{\circ}i=$

$=2\sin 15^{\circ}(\sin 15^{\circ}+i\cos 15^{\circ})= 2\sin (45^{\circ}-30^{\circ})(\cos 75^{\circ}+i\sin 75^{\circ})=$

$2(\sin 45^{\circ}\cos 30^{\circ}-\cos 45^{\circ}\sin 30^{\circ})(\cos 75^{\circ}+i\sin 75^{\circ})=$

$=\frac{\sqrt{6}-\sqrt{2}}{2}(\cos 75^{\circ}+i\sin 75^{\circ})$