Solve the problem. Leave your answer in polar form.
-$$\begin{array} { l }
\left. z = 6 \cos \frac { 3 \pi } { 2 } + i \sin \frac { 3 \pi } { 2 } \right) \
w = 12 \left( \cos \frac { 5 \pi } { 6 } + i \sin \frac { 5 \pi } { 6 } \right)
\end{array}$$
Find zw.
A) $36 \left( \cos \frac { \pi } { 6 } + i \sin \frac { \pi } { 6 } \right)$
B) $72 \left( \cos \frac { \pi } { 6 } + i \sin \frac { \pi } { 6 } \right)$
C) $36 \left( \cos \frac { \pi } { 3 } + i \sin \frac { \pi } { 3 } \right)$
D) $72 \left( \cos \frac { \pi } { 3 } + i \sin \frac { \pi } { 3 } \right)$

Question

Solve the problem. Leave your answer in polar form.
-$$\begin{array} { l } 
\left. z = 6 \cos \frac { 3 \pi } { 2 } + i \sin \frac { 3 \pi } { 2 } \right) \
w = 12 \left( \cos \frac { 5 \pi } { 6 } + i \sin \frac { 5 \pi } { 6 } \right)
\end{array}$$
Find zw.
A) $36 \left( \cos \frac { \pi } { 6 } + i \sin \frac { \pi } { 6 } \right)$
B) $72 \left( \cos \frac { \pi } { 6 } + i \sin \frac { \pi } { 6 } \right)$
C) $36 \left( \cos \frac { \pi } { 3 } + i \sin \frac { \pi } { 3 } \right)$
D) $72 \left( \cos \frac { \pi } { 3 } + i \sin \frac { \pi } { 3 } \right)$

Quizplus · Accepted Answer

To find zw, multiply the magnitudes and add the angles: $6 \times 12 = 72$ and $\frac{3\pi}{2} + \frac{5\pi}{6} = \frac{9\pi}{3} + \frac{5\pi}{6} = \frac{18\pi}{6} + \frac{5\pi}{6} = \frac{23\pi}{6}$. Simplify the angle to $\frac{\pi}{3}$ (since $\frac{23\pi}{6} - 2\pi = \frac{\pi}{3}$). Thus, the answer is $72 \left( \cos \frac{\pi}{3} + i \sin \frac{\pi}{3} \right)$.

Solve the Problem Find Zw A) 36(cos⁡π6+isin⁡π6)36 \left( \cos \frac { \pi } { 6 } + i \sin \frac { \pi } { 6 } \right)36(cos6π​+isin6π​)

Solve the Problem Find Zw
A) $36 \left( \cos \frac { \pi } { 6 } + i \sin \frac { \pi } { 6 } \right)$