Perform the indicated operation. Give answers in rectangular form expressing real and imaginary parts to four decimal
places.
-$\left[ 5 \operatorname { cis } \frac { 4 \pi } { 9 } \right] ^ { 2 }$
A) $- 23.4923 + 8.5505 i$
B) $8.5505 - 23.4923 \mathrm { i }$
C) $- 4.6985 + 1.7101 \mathrm { i }$
D) $4.3412 + 24.6202 \mathrm { i }$

Question

Quizplus · Accepted Answer

When raising a complex number in polar form, $r(\cos \theta + i\sin \theta)$, to a power $n$, you use De Moivre's Theorem: $(r(\cos \theta + i\sin \theta))^n = r^n(\cos(n\theta) + i\sin(n\theta))$. Here, $r = 5$, $\theta = \frac{4\pi}{9}$, and $n = 2$. Thus, $5^2(\cos(2 \cdot \frac{4\pi}{9}) + i\sin(2 \cdot \frac{4\pi}{9}))$. Calculating this gives $- 23.4923 + 8.5505 i$.

Perform the Indicated Operation [5cis⁡4π9]2\left[ 5 \operatorname { cis } \frac { 4 \pi } { 9 } \right] ^ { 2 }[5cis94π​]2

Perform the Indicated Operation $\left[ 5 \operatorname { cis } \frac { 4 \pi } { 9 } \right] ^ { 2 }$