Find All Specified Roots $i$
A) B) $1 , - 1 , i , - i$

question 274

Multiple Choice

Find all specified roots.
-Eighth roots of $i$ .

• A) \(\frac { 1 } { \sqrt { 2 } } + \frac { 1 } { \sqrt { 2 } } \mathrm { i } , \frac { 1 } { \sqrt { 2 } } - \frac { 1 } { \sqrt { 2 } } \mathrm { i } , - \frac { 1 } { \sqrt { 2 } } + \frac { 1 } { \sqrt { 2 } } \mathrm { i } , - \frac { 1 } { \sqrt { 2 } } - \frac { 1 } { \sqrt { 2 } } \mathrm { i }\)
• B) \(1 , - 1 , i , - i\)
• C) \(\operatorname { cis } \frac { \pi } { 16 } , \operatorname { cis } \frac { 5 \pi } { 16 } , \operatorname { cis } \frac { 9 \pi } { 16 } , \operatorname { cis } \frac { 13 \pi } { 16 } , \operatorname { cis } \frac { 17 \pi } { 16 }\), cis \(\frac { 21 \pi } { 16 } , \operatorname { cis } \frac { 25 \pi } { 16 } , \operatorname { cis } \frac { 29 \pi } { 16 }\)
• D) \(1 , - 1 , i , - i , \frac { 1 } { \sqrt { 2 } } + \frac { 1 } { \sqrt { 2 } } i , \frac { 1 } { \sqrt { 2 } } - \frac { 1 } { \sqrt { 2 } } \mathrm { i } , - \frac { 1 } { \sqrt { 2 } } + \frac { 1 } { \sqrt { 2 } } \mathrm { i } , - \frac { 1 } { \sqrt { 2 } } - \frac { 1 } { \sqrt { 2 } } \mathrm { i }\)

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Definitions:

Long-Run Equilibrium

A state in which market supply equals market demand and all firms in a perfectly competitive market earn zero economic profits.

Elastic Demand

A situation in which demand for a product or service is sensitive to price changes, meaning a small change in price can lead to a significant change in quantity demanded.

Revenue Generation

The process of creating income for a business or organization through various means such as sales, services, or investments.

Lower Fares

Reduced charges for services, particularly in transportation, such as airfares or bus tickets, making travel more affordable.