Find all cube roots of the complex number. Leave answers in trigonometric form.
-$$2 + 2 i \sqrt { 3 }$$
A) $\sqrt [ 3 ] { 4 } \operatorname { cis } 30 ^ { \circ } , \sqrt [ 3 ] { 4 } \operatorname { cis } 150 ^ { \circ } , \sqrt [ 3 ] { 4 } \operatorname { cis } 270 ^ { \circ }$
B) $\sqrt [ 3 ] { 4 } \operatorname { cis } 20 ^ { \circ } , \sqrt [ 3 ] { 4 } \operatorname { cis } 140 ^ { \circ } , \sqrt [ 3 ] { 4 } \operatorname { cis } 260 ^ { \circ }$
C) $\sqrt { 2 } \operatorname { cis } 20 ^ { \circ } , \sqrt { 2 } \operatorname { cis } 140 ^ { \circ } , \sqrt { 2 } \operatorname { cis } 260 ^ { \circ }$
D) $\sqrt { 4 } \operatorname { cis } 20 ^ { \circ } , \sqrt { 4 } \operatorname { cis } 140 ^ { \circ } , \sqrt { 4 } \operatorname { cis } 260 ^ { \circ }$

Question

Quizplus · Accepted Answer

The complex number $2 + 2i\sqrt{3}$ can be expressed in polar form as $4 \operatorname{cis} 60^\circ$. The cube roots are $\sqrt[3]{4} \operatorname{cis} \left(\frac{60^\circ + 360^\circ k}{3}\right)$ for $k = 0, 1, 2$, which gives the angles $20^\circ, 140^\circ, 260^\circ$.

Find All Cube Roots of the Complex Number 2+2i32 + 2 i \sqrt { 3 }2+2i3​

Find All Cube Roots of the Complex Number $2 + 2 i \sqrt { 3 }$