Question

Помоги решить 5 задание

Answer 1

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

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

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

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