Find All Cube Roots of the Complex Number $4 - 4 i \sqrt { 3 }$

question 127

Multiple Choice

Find all cube roots of the complex number. Leave answers in trigonometric form.
- $4 - 4 i \sqrt { 3 }$

• A) \(\sqrt [ 3 ] { 4 } \operatorname { cis } 80 ^ { \circ } , \sqrt [ 3 ] { 4 } \operatorname { cis } 200 ^ { \circ } , \sqrt [ 3 ] { 4 } \operatorname { cis } 320 ^ { \circ }\)
• B) \(\sqrt { 8 } \operatorname { cis } 100 ^ { \circ } , \sqrt { 8 } \operatorname { cis } 220 ^ { \circ } , \sqrt { 8 } \operatorname { cis } 340 ^ { \circ }\)
• C) \(\sqrt [ 3 ] { 8 } \operatorname { cis } 100 ^ { \circ } , \sqrt [ 3 ] { 8 } \operatorname { cis } 220 ^ { \circ } , \sqrt [ 3 ] { 8 } \operatorname { cis } 340 ^ { \circ }\)
• D) \(\sqrt { 4 } \operatorname { cis } 60 ^ { \circ } , \sqrt { 4 } \operatorname { cis } 180 ^ { \circ } , \sqrt { 4 } \operatorname { cis } 300 ^ { \circ }\)

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Definitions:

Irreversibility

The cognitive inability in children to understand that actions can be reversed to return to the original state.

Piagetian Characteristic

Pertaining to the developmental stages and theories of cognitive development introduced by Jean Piaget.

Critical Period

A specific time in an organism's development during which the presence or absence of certain experiences can have long-lasting effects on future development.