Accedmychevron_right11thchevron_rightmathchevron_rightComplex Numberschevron_rightExercise 1.5

(iv) z1z2\dfrac{z_1}{z_2}

z1z2=95(cos11π12+isin11π12)\frac{z_1}{z_2}=\frac{9}{5}\left(\cos\frac{11\pi}{12}+i\sin\frac{11\pi}{12}\right) cos11π12=6+24,sin11π12=624\cos\frac{11\pi}{12}=-\frac{\sqrt{6}+\sqrt{2}}{4},\quad \sin\frac{11\pi}{12}=\frac{\sqrt{6}-\sqrt{2}}{4} z1z2=9(6+2)20+9(62)20i\boxed{\frac{z_1}{z_2}=-\frac{9(\sqrt{6}+\sqrt{2})}{20}+\frac{9(\sqrt{6}-\sqrt{2})}{20}i}