Find All Solutions of the Equation $$x ^ { 4 } + 16 i = 0$$

question 232

Multiple Choice

Find all solutions of the equation. Leave answers in trigonometric form.
- $$x ^ { 4 } + 16 i = 0$$

• A) \(\left\{ 2 \operatorname { cis } \frac { 3 \pi } { 8 } , 2 \operatorname { cis } \frac { 7 \pi } { 8 } , 2 \operatorname { cis } \frac { 11 \pi } { 8 } , 2 \operatorname { cis } \frac { 15 \pi } { 8 } \right\}\)
• B) \(\left\{ \operatorname { cis } \frac { 3 \pi } { 8 } , \operatorname { cis } \frac { 7 \pi } { 8 } , \operatorname { cis } \frac { 11 \pi } { 8 } , \operatorname { cis } \frac { 15 \pi } { 8 } \right\}\)
• C) \(\left\{ 16 \operatorname { cis } \frac { 3 \pi } { 8 } , 16 \operatorname { cis } \frac { 7 \pi } { 8 } , 16 \operatorname { cis } \frac { 11 \pi } { 8 } , 16 \operatorname { cis } \frac { 15 \pi } { 8 } \right\}\)
• D) \(\{ 1 , - 1 , i , - i \}\)

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Definitions:

Time Discipline

The social and economic practice of coordinating and regulating human activities and work efficiency through the strict measurement and management of time.

Labor Movement

A socio-political movement advocating for the rights and interests of workers, including better working conditions, higher wages, and collective bargaining.

South

A reference often used in the context of the United States to designate the southeastern states, historically characterized by their support for slavery and later segregation.

Abolitionists

Individuals or groups advocating for the immediate end of slavery and the emancipation of slaves, active primarily in the 18th and 19th centuries.