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

question 24

Multiple Choice

Use DeMoivre's Theorem to find the indicated power of the following complex number.
$$( 5 + 5 \sqrt { 3 } i ) ^ { 6 }$$

• A) \(1,953,125\)
• B) 390,625
• C) 78,125
• D) \(1,000,000\)
• E) 3,125

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Definitions:

Psychomotor Retardation

A significant slowing-down of thought and a reduction of physical movements in an individual, often observed in major depressive disorder.

Psychomotor Agitation

A condition characterized by increased physical and emotional tension, often manifesting in restless and repetitive movements.

Psychomotor Atrophy

The deterioration of cognitive, emotional, and physical abilities due to underutilization or neuron degeneration.

Psychotic

Relating to psychosis, a mental disorder characterized by a disconnection from reality, which may include hallucinations and delusions.