Multiply the Complex Numbers Below and Leave the Result in Trigonometric

question 263

Multiple Choice

Multiply the complex numbers below and leave the result in trigonometric form. $\left[ 8 \left( \cos \frac { 2 \pi } { 7 } + i \sin \frac { 2 \pi } { 7 } \right) \right] \left[ 10 \left( \cos \frac { 5 \pi } { 9 } + i \sin \frac { 5 \pi } { 9 } \right) \right]$

• A) \(18 \left( \cos \frac { 53 } { 63 } \pi + i \sin \frac { 53 } { 63 } \pi \right)\)
• B) \(80 \left( \cos \frac { 23 } { 63 } \pi + i \sin \frac { 23 } { 63 } \pi \right)\)
• C) \(80 \left( \cos \frac { 53 } { 63 } \pi + i \sin \frac { 53 } { 63 } \pi \right)\)
• D) \(18 \left( \cos \frac { 1 } { 9 } \pi + i \sin \frac { 1 } { 9 } \pi \right)\)
• E) \(80 \left( \cos \frac { 1 } { 9 } \pi + i \sin \frac { 1 } { 9 } \pi \right)\)

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Definitions:

Apparent Authority

A situation in which a person appears to have been given the power by another party to act on their behalf, leading third parties to reasonably believe that authority exists.

Partnership Agreement

A contract among business partners detailing the business structure, distribution of profits and losses, and rules for the partnership's governance and operation.

Formal Resolution

An official decision or declaration adopted by an organization or assembly through a formal process.

Nontrading Partnership

A partnership focused on activities other than buying and selling goods, such as investment or professional services.