Solve the problem. Leave your answer in polar form.
-$$\begin{array} { l }
z = 10 \left( \cos 45 ^ { \circ } + i \sin 45 ^ { \circ } \right) \
w = 5 \left( \cos 15 ^ { \circ } + i \sin 15 ^ { \circ } \right)
\end{array}$$
Find $\frac { z } { w }$.
A) $2 \left( \cos 30 ^ { \circ } + i \sin 30 ^ { \circ } \right)$
B) $\frac { 1 } { 2 } \left( \cos 30 ^ { \circ } + i \sin 30 ^ { \circ } \right)$
C) $\frac { 1 } { 2 } \left( \cos 45 ^ { \circ } + i \sin 45 ^ { \circ } \right)$
D) $2 \left( \cos 45 ^ { \circ } + \mathrm { i } \sin 45 ^ { \circ } \right)$

Question

Solve the problem. Leave your answer in polar form.
-$$\begin{array} { l } 
z = 10 \left( \cos 45 ^ { \circ } + i \sin 45 ^ { \circ } \right) \
w = 5 \left( \cos 15 ^ { \circ } + i \sin 15 ^ { \circ } \right)
\end{array}$$
Find $\frac { z } { w }$.
A) $2 \left( \cos 30 ^ { \circ } + i \sin 30 ^ { \circ } \right)$
B) $\frac { 1 } { 2 } \left( \cos 30 ^ { \circ } + i \sin 30 ^ { \circ } \right)$
C) $\frac { 1 } { 2 } \left( \cos 45 ^ { \circ } + i \sin 45 ^ { \circ } \right)$
D) $2 \left( \cos 45 ^ { \circ } + \mathrm { i } \sin 45 ^ { \circ } \right)$

Quizplus · Accepted Answer

To divide two complex numbers in polar form, you divide their magnitudes and subtract their angles. Here, $\frac{z}{w} = \frac{10}{5} \left( \cos (45^\circ - 15^\circ) + i \sin (45^\circ - 15^\circ) \right) = 2 \left( \cos 30^\circ + i \sin 30^\circ \right)$.

Solve the Problem Find zw\frac { z } { w }wz​

Solve the Problem Find $\frac { z } { w }$