Find Powers of Complex Numbers in Polar Form
- $$\left[ 3 \left( \cos 15 ^ { \circ } + i \sin 15 ^ { \circ } \right) \right] ^ { 4 }$$

question 49

Multiple Choice

Find Powers of Complex Numbers in Polar Form
- $$\left[ 3 \left( \cos 15 ^ { \circ } + i \sin 15 ^ { \circ } \right) \right] ^ { 4 }$$

• A) \(\frac { 81 } { 2 } + \frac { 81 \sqrt { 3 } } { 2 } \mathrm { i }\)
• B) \(\frac { 81 } { 2 } + \frac { 81 } { 2 } \mathrm { i }\)
• C) \(\frac { 81 \sqrt { 3 } } { 2 } + \frac { 81 } { 2 } \mathrm { i }\)
• D) \(81 \mathrm { i }\)

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Definitions:

Monopolistically Competitive

A market structure characterized by many firms, differentiated products, and free entry and exit, allowing firms some control over price while still competing on quality, branding, and price.

Externality

A cost or benefit that affects a third party who did not choose to incur that cost or benefit.

Efficient Scale

The level of production at which a firm's average total costs are minimized.

Monopolistically Competitive

A market structure where many sellers offer products or services that are similar but not perfect substitutes, allowing for some degree of market power.