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:

Collection Float

The time period between when a check is deposited in a bank and when the funds are made available, reflecting the bank's processing time.

Mail Float

The time difference between when a check is written and when it is actually cleared and funds are deducted from the payer's account.

Availability Float

The time difference between when a check is deposited in a bank account and when the funds are made available.

Miller-Orr Model

A financial model used to manage cash balances by setting upper and lower limits on cash reserves, triggering buying or selling of securities when these thresholds are crossed.