Accedmychevron_right11thchevron_rightmathchevron_rightComplex Numberschevron_rightExercise 1.5

(ii)

z=32(cos7π6+isin7π6)z=\frac{3}{2}\left(\cos\frac{7\pi}{6}+i\sin\frac{7\pi}{6}\right) cos7π6=32,sin7π6=12\cos\frac{7\pi}{6}=-\frac{\sqrt{3}}{2},\quad \sin\frac{7\pi}{6}=-\frac{1}{2} z=32(3212i)=33434i\boxed{z=\frac{3}{2}\left(-\frac{\sqrt{3}}{2}-\frac{1}{2}i\right)=-\frac{3\sqrt{3}}{4}-\frac{3}{4}i}