Find Quotients of Complex Numbers in Polar Form
-$$\begin{array} { l }
\mathrm { z } 1 = 5 \left( \cos 200 ^ { \circ } + \mathrm { i } \sin 200 ^ { \circ } \right) \
\mathrm { z } _ { 2 } = 4 \left( \cos 50 ^ { \circ } + \mathrm { i } \sin 50 ^ { \circ } \right)
\end{array}$$
A) $\frac { 5 } { 4 } \left( \cos 150 ^ { \circ } + i \sin 150 ^ { \circ } \right)$
B) $\frac { 5 } { 4 } \left( \cos 250 ^ { \circ } + i \sin 250 ^ { \circ } \right)$
C) $\frac { 5 } { 4 } \left( \cos 150 ^ { \circ } - \mathrm { i } \sin 150 ^ { \circ } \right)$
D) $\frac { 5 } { 4 } \left( \sin 150 ^ { \circ } + i \cos 150 ^ { \circ } \right)$

Question

Find Quotients of Complex Numbers in Polar Form
-$$\begin{array} { l } 
\mathrm { z } 1 = 5 \left( \cos 200 ^ { \circ } + \mathrm { i } \sin 200 ^ { \circ } \right) \
\mathrm { z } _ { 2 } = 4 \left( \cos 50 ^ { \circ } + \mathrm { i } \sin 50 ^ { \circ } \right)
\end{array}$$
A) $\frac { 5 } { 4 } \left( \cos 150 ^ { \circ } + i \sin 150 ^ { \circ } \right)$
B) $\frac { 5 } { 4 } \left( \cos 250 ^ { \circ } + i \sin 250 ^ { \circ } \right)$
C) $\frac { 5 } { 4 } \left( \cos 150 ^ { \circ } - \mathrm { i } \sin 150 ^ { \circ } \right)$
D) $\frac { 5 } { 4 } \left( \sin 150 ^ { \circ } + i \cos 150 ^ { \circ } \right)$

Quizplus · Accepted Answer

To divide two complex numbers in polar form, divide their magnitudes and subtract their angles. Thus, the quotient is $\frac{5}{4}(\cos(200^\circ - 50^\circ) + i\sin(200^\circ - 50^\circ)) = \frac{5}{4}(\cos 150^\circ + i\sin 150^\circ)$.

Find Quotients of Complex Numbers in Polar Form - A) 54(cos⁡150∘+isin⁡150∘)\frac { 5 } { 4 } \left( \cos 150 ^ { \circ } + i \sin 150 ^ { \circ } \right)45​(cos150∘+isin150∘)

Find Quotients of Complex Numbers in Polar Form
- A) $\frac { 5 } { 4 } \left( \cos 150 ^ { \circ } + i \sin 150 ^ { \circ } \right)$