Question

Find the cube roots of -64 i. Graph each cube root as a vector in the complex plane. Choose the correct cube roots below. O A. 64(cos 60° + i sin 60%), 64(cos 180° + i sin 180°), 64(cos 300° + i sin 300°) OB. 4(cos 30° + i sin 300), 4(cos 150° + i sin 150°), 4(cos 270° + i sin 270º) OC. 4(cos 90° + i sin 90°), 4(cos 210° + i sin 210), 4(cos 330° + i sin 330°) OD. 64(cos 0° + i sin 0°), 64(cos 120° + i sin 120°), 64(cos 240° + i sin 240°) Choose the correct graph of the cube roots of - 64 i below. OA. OB. OC. OD.

Answer 1

0 Ginen 2= -bu i 64 (0 + (-1)) Z - (cos 37 64 i sin 37 + 3 De According to Moivre's Formula . 36 Cos akhto + i Siu 2kato Z 3 Now, put K=o ZE u (cas cas 31 - 1 2 , Put kal 2₂= ۹ t + i sin BI *) 4 (cs I ti sim 1 *z=(Cosgo't isiwgoy (can 12+ 31 1 ti sim ***23) (cos Cosz10' + i sim 210°) " ( cas 6x + 2 + i sin box + 2 1 1 2 4 (Cos 3309+ i sin 3 30"). u cos Za i sin Ihr + 22 Put K=2. 23 z Zz

NOW, All thre cube woth are 9 u(cs goʻ+ i sin go") u (Cos2100+ i sin 210) and ulCos 330°t i sin 330%) option corect () นา Graph As, 4 (Corgo tê sin goo) = 4i. so, op Hom is correct