Find all specified roots.
-Sixth roots of i.
A) $\operatorname { cis } \frac { 3 \pi } { 4 } , \operatorname { cis } \frac { 17 \pi } { 12 } , \operatorname { cis } \frac { 25 \pi } { 12 } , \operatorname { cis } \frac { 11 \pi } { 4 } , \mathrm { i }$
B) $\operatorname { cis } \frac { \pi } { 12 } , \operatorname { cis } \frac { 3 \pi } { 4 } , \operatorname { cis } \frac { 17 \pi } { 12 } , \operatorname { cis } \frac { 25 \pi } { 12 }$
C) $\operatorname { cis } \frac { \pi } { 12 } , \operatorname { cis } \frac { 3 \pi } { 4 } , \operatorname { cis } \frac { 17 \pi } { 12 } , \operatorname { cis } \frac { 25 \pi } { 12 } , \operatorname { cis } \frac { 11 \pi } { 4 } , 1$
D) $\operatorname { cis } \frac { \pi } { 12 } , \operatorname { cis } \frac { 5 \pi } { 12 } , \operatorname { cis } \frac { 3 \pi } { 4 } , \operatorname { cis } \frac { 7 \pi } { 4 } , \operatorname { cis } \frac { 13 \pi } { 12 } , \frac { 17 \pi } { 12 }$

Question

Quizplus · Accepted Answer

The sixth roots of $i$ are found by expressing $i$ in polar form as $\operatorname{cis} \frac{\pi}{2}$ and using the formula for nth roots: $\operatorname{cis} \frac{\pi}{2n} + \frac{2k\pi}{n}$ for $k = 0, 1, ..., n-1$. For $n = 6$, this gives the angles $\frac{\pi}{12}, \frac{5\pi}{12}, \frac{3\pi}{4}, \frac{7\pi}{12}, \frac{13\pi}{12}, \frac{17\pi}{12}$.

Find All Specified Roots B) C) D)