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

question 75

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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