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:

Storge

Solid love found in friendships and family, based on trust and caring.

Ludus

Game-playing love based on the enjoyment of another.

Pragma

Practical love based on mutual benefits.

Storge

A term referring to love that is based on friendship, familial bonds, and familiarity, rather than romantic or physical attraction.