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

question 114

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

---

Definitions:

Vitamin D

A fat-soluble vitamin that is vital for maintaining healthy bones and teeth, supporting the immune system, and regulating insulin levels.

Metabolic Syndrome

A cluster of conditions including increased blood pressure, high blood sugar, excess body fat around the waist, and abnormal cholesterol levels, that occur together, increasing your risk of heart disease, stroke, and diabetes.

High-Density Lipoprotein

Often referred to as "good" cholesterol; a type of lipoprotein that helps remove other forms of cholesterol from the bloodstream.

Fasting Blood Glucose

A measure of the sugar levels in blood after an individual has not eaten for a specific period, usually 8 hours, important for diagnosing diabetes.