Use DeMoivre's Theorem to Find the Indicated Power of the Complex

question 22

Multiple Choice

Use DeMoivre's Theorem to find the indicated power of the complex number.Write the result in standard form. $\left[ - 5 \left( \cos \left( 210 ^ { \circ } \right) + i \sin \left( 210 ^ { \circ } \right) \right) \right] ^ { 10 }$

• A) \(- \frac { 9765625 } { 2 } + \frac { 9765625 \sqrt { 3 } } { 2 } i\)
• B) \(\frac { 9765625 } { 2 } + \frac { 9765625 \sqrt { 3 } } { 2 } i\)
• C) \(\frac { 9765625 } { 2 } - \frac { 9765625 \sqrt { 3 } } { 2 } i\)
• D) \(\frac { 9765625 \sqrt { 3 } } { 2 } - \frac { 9765625 } { 2 } i\)
• E) \(- \frac { 9765625 \sqrt { 3 } } { 2 } + \frac { 9765625 } { 2 } i\)

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Definitions:

Priority

The order in which rights, obligations, or claims are ranked or considered, often in a legal context.

Default

Failure to fulfill a duty or obligation, typically in the context of financial agreements such as failing to make loan payments.

Obtaining Control

The act of gaining the power or authority to manage or direct something or someone.

Collateral

Assets pledged by a borrower to secure a loan or credit, which the lender may seize if the borrower fails to repay the loan.