Find the given power. Write answer in rectangular form.
-$\left[ 2 \operatorname { cis } 15 ^ { \circ } \right] ^ { 4 }$
A) $8 + 8 i \sqrt { 3 }$
B) $16 \mathrm { i }$
C) $8 + 8 \mathrm { i }$
D) $8 \sqrt { 3 } + 8 i$

Question

Quizplus · Accepted Answer

Using De Moivre's Theorem, $\left[ r \operatorname { cis } \theta \right] ^ { n } = r ^ { n } \operatorname { cis } ( n \theta )$, for $\left[ 2 \operatorname { cis } 15 ^ { \circ } \right] ^ { 4 }$, we get $16 \operatorname { cis } 60 ^ { \circ }$. Converting to rectangular form, $16(\cos 60^\circ + i\sin 60^\circ) = 16(\frac{1}{2} + i\frac{\sqrt{3}}{2}) = 8 + 8i\sqrt{3}$.

Find the Given Power [2cis⁡15∘]4\left[ 2 \operatorname { cis } 15 ^ { \circ } \right] ^ { 4 }[2cis15∘]4

Find the Given Power $\left[ 2 \operatorname { cis } 15 ^ { \circ } \right] ^ { 4 }$