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

question 6

Multiple Choice

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

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

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Definitions:

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