Find all cube roots of the complex number. Leave answers in trigonometric form.
-$$- 64 i$$
A) $4 \operatorname { cis } 90 ^ { \circ } , 4$ cis $^ { \circ } 210,4$ cis $330 ^ { \circ }$
B) 4 cis $90 ^ { \circ } , 4 \operatorname { cis } ^ { \circ } 180,4$ cis $270 ^ { \circ }$
C) $4 \operatorname { cis } 30 ^ { \circ } , 4$ cis $^ { \circ } 60,4 \operatorname { cis } 90 ^ { \circ }$
D) 4 cis ${ } ^ { \circ } 210 , , 4 \operatorname { cis } 270 ^ { \circ } , 4 \operatorname { cis } 330 ^ { \circ }$

Question

Quizplus · Accepted Answer

The complex number $-64i$ can be written in polar form as $64\operatorname{cis}270^\circ$. To find its cube roots, we divide the angle by 3 and find all roots spaced evenly around the circle. Thus, the cube roots are $4\operatorname{cis}90^\circ$, $4\operatorname{cis}210^\circ$, and $4\operatorname{cis}330^\circ$.

Find All Cube Roots of the Complex Number −64i- 64 i−64i

Find All Cube Roots of the Complex Number $- 64 i$