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

question 128

Multiple Choice

Find all cube roots of the complex number. Leave answers in trigonometric form.
- $$2 + 2 \mathrm { i } \sqrt { 3 }$$

• A) \(\sqrt [ 3 ] { 4 } \operatorname { cis } 30 ^ { \circ } , \sqrt [ 3 ] { 4 } \operatorname { cis } 150 ^ { \circ } , \sqrt [ 3 ] { 4 } \operatorname { cis } 270 ^ { \circ }\)
• B) \(\sqrt { 4 } \operatorname { cis } 20 ^ { \circ } , \sqrt { 4 } \operatorname { cis } 140 ^ { \circ } , \sqrt { 4 } \operatorname { cis } 260 ^ { \circ }\)
• C) \(\sqrt [ 3 ] { 4 } \operatorname { cis } 20 ^ { \circ } , \sqrt [ 3 ] { 4 } \operatorname { cis } 140 ^ { \circ } , \sqrt [ 3 ] { 4 } \operatorname { cis } 260 ^ { \circ }\)
• D) \(\sqrt { 2 } \operatorname { cis } 20 ^ { \circ } , \sqrt { 2 } \operatorname { cis } 140 ^ { \circ } , \sqrt { 2 } \operatorname { cis } 260 ^ { \circ }\)

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Definitions:

Thyroid Gland

An endocrine gland located in the neck that produces hormones regulating metabolism and energy level.

Poisonous Condition

A state of health impairment caused by the ingestion, inhalation, or absorption of toxic substances.

Potassium

An essential mineral and electrolyte necessary for the proper functioning of cells, nerves, and muscles in the body.

Excessive Amounts

Quantities that exceed what is normal, necessary, or reasonable.