Find Quotients of Complex Numbers in Polar Form
-$$\begin{array} { l }
z 1 = \frac { 1 } { 2 } \left( \cos \frac { 2 \pi } { 3 } + i \sin \frac { 2 \pi } { 3 } \right) \
z 2 = \frac { 1 } { 7 } \left( \cos \frac { \pi } { 4 } + i \sin \frac { \pi } { 4 } \right)
\end{array}$$
A) $\frac { 7 } { 2 } \left( \cos \frac { 5 \pi } { 12 } + i \sin \frac { 5 \pi } { 12 } \right)$
B) $\frac { 1 } { 14 } \left( \cos \frac { 11 \pi } { 12 } + i \sin \frac { 11 \pi } { 12 } \right)$
C) $\frac { 7 } { 2 } \left( \cos \frac { 8 } { 3 } + i \sin \frac { 8 } { 3 } \right)$
D) $\frac { 2 } { 7 } \left( \cos - \frac { 5 \pi } { 12 } + i \sin - \frac { 5 \pi } { 12 } \right)$

Question

Find Quotients of Complex Numbers in Polar Form
-$$\begin{array} { l } 
z 1 = \frac { 1 } { 2 } \left( \cos \frac { 2 \pi } { 3 } + i \sin \frac { 2 \pi } { 3 } \right) \
z 2 = \frac { 1 } { 7 } \left( \cos \frac { \pi } { 4 } + i \sin \frac { \pi } { 4 } \right)
\end{array}$$
A) $\frac { 7 } { 2 } \left( \cos \frac { 5 \pi } { 12 } + i \sin \frac { 5 \pi } { 12 } \right)$
B) $\frac { 1 } { 14 } \left( \cos \frac { 11 \pi } { 12 } + i \sin \frac { 11 \pi } { 12 } \right)$
C) $\frac { 7 } { 2 } \left( \cos \frac { 8 } { 3 } + i \sin \frac { 8 } { 3 } \right)$
D) $\frac { 2 } { 7 } \left( \cos - \frac { 5 \pi } { 12 } + i \sin - \frac { 5 \pi } { 12 } \right)$

Quizplus · Accepted Answer

To divide two complex numbers in polar form, you divide their magnitudes and subtract their angles. Here, the magnitudes are $1/2$ and $1/7$, so their quotient is $\frac{1/2}{1/7} = \frac{7}{2}$. The angles are $2\pi/3$ and $\pi/4$, so their difference is $2\pi/3 - \pi/4 = 8\pi/12 - 3\pi/12 = 5\pi/12$. Therefore, the quotient in polar form is $\frac{7}{2}(\cos(5\pi/12) + i\sin(5\pi/12))$.

Find Quotients of Complex Numbers in Polar Form - A) 72(cos⁡5π12+isin⁡5π12)\frac { 7 } { 2 } \left( \cos \frac { 5 \pi } { 12 } + i \sin \frac { 5 \pi } { 12 } \right)27​(cos125π​+isin125π​)

Find Quotients of Complex Numbers in Polar Form
- A) $\frac { 7 } { 2 } \left( \cos \frac { 5 \pi } { 12 } + i \sin \frac { 5 \pi } { 12 } \right)$