Use De Moivre's Theorem to Find the Indicated Power of the Complex

question 5

Multiple Choice

Use De Moivre's Theorem to find the indicated power of the complex number. Write your answer in standard form a + bi.
- $\left( 5 \left( \cos 70 ^ { \circ } + i \sin 70 ^ { \circ } \right) \right) ^ { 3 }$

• A) \(- 108.25 - 62.5 \mathrm { i }\)
• B) \(- 12.99 - 62.5 \mathrm { i }\)
• C) \(- 170.75\)
• D) \(- 12.99 + 62.5 \mathrm { i }\)

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Definitions:

Marginal Cost Curve

A graphical representation showing the change in total production cost resulting from producing one additional unit of a good.

Upward-Sloping

Typically refers to the positive slope of a supply curve in economics, indicating that as the price increases, the quantity supplied also increases.

Output

The collective volume of products or services generated by an enterprise, sector, or economic system.

Average-Total-Cost Curve

A graphical representation showing the average cost per unit of output at different levels of production, typically U-shaped due to economies and diseconomies of scale.