Find all cube roots of the complex number. Leave answers in trigonometric form.
-$- 125 \mathrm { i }$
A) $5 \operatorname { cis } ^ { \circ } 210,5 \operatorname { cis } 270 ^ { \circ } , 5 \operatorname { cis } 330 ^ { \circ }$
B) $5 \operatorname { cis } 30 ^ { \circ } , 5 \operatorname { cis } ^ { \circ } 60,5 \operatorname { cis } 90 ^ { \circ }$
C) $5 \operatorname { cis } 90 ^ { \circ } , 5 \operatorname { cis } ^ { \circ } 180,5 \operatorname { cis } 270 ^ { \circ }$
D) $5 \operatorname { cis } 90 ^ { \circ } , 5 \operatorname { cis } ^ { \circ } 210,5 \operatorname { cis } 330 ^ { \circ }$

Question

Quizplus · Accepted Answer

The complex number $-125i$ can be written in polar form as $125\operatorname{cis}270^\circ$. To find the cube roots, we divide the angle by 3 and find all roots spaced evenly around the circle. The roots are $5\operatorname{cis}90^\circ$, $5\operatorname{cis}210^\circ$, and $5\operatorname{cis}330^\circ$.

Find All Cube Roots of the Complex Number −125i- 125 \mathrm { i }−125i

Find All Cube Roots of the Complex Number $- 125 \mathrm { i }$