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Find All Solutions of the Equation x4+16i=0x ^ { 4 } + 16 i = 0

Question 6

Multiple Choice

Find all solutions of the equation. Leave answers in trigonometric form.
- x4+16i=0x ^ { 4 } + 16 i = 0


A) {cis3π8,cis7π8,cis11π8,cis15π8}\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) {16cis3π8,16cis7π8,16cis11π8,16cis15π8}\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) {2cis3π8,2cis7π8,2cis11π8,2cis15π8}\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}\{ 1 , - 1 , i , - i \}

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