Find the quotient and write in rectangular form. First convert the numerator and denominator to trigonometric form.
-$$\frac { 5 \left( \cos 200 ^ { \circ } + i \sin 200 ^ { \circ } \right) } { 4 \left( \cos 50 ^ { \circ } + i \sin 50 ^ { \circ } \right) }$$
A) $- 10 + 10 \sqrt { 3 } i$
B) $- \frac { 5 \sqrt { 3 } } { 8 } + \frac { 5 } { 8 } i$
C) $- 2 + 2 \sqrt { 3 } i$
D) $- \frac { 1 } { 2 } + \frac { \sqrt { 3 } } { 2 } \mathrm { i }$

Question

Quizplus · Accepted Answer

To divide complex numbers in trigonometric form, divide the magnitudes and subtract the angles. Here, the quotient is $\frac{5}{4}(\cos(200^\circ - 50^\circ) + i\sin(200^\circ - 50^\circ)) = \frac{5}{4}(\cos(150^\circ) + i\sin(150^\circ))$. Converting this to rectangular form gives $-\frac{5\sqrt{3}}{8} + \frac{5}{8}i$.

Find the Quotient and Write in Rectangular Form 5(cos⁡200∘+isin⁡200∘)4(cos⁡50∘+isin⁡50∘)\frac { 5 \left( \cos 200 ^ { \circ } + i \sin 200 ^ { \circ } \right) } { 4 \left( \cos 50 ^ { \circ } + i \sin 50 ^ { \circ } \right) }4(cos50∘+isin50∘)5(cos200∘+isin200∘)​

Find the Quotient and Write in Rectangular Form $\frac { 5 \left( \cos 200 ^ { \circ } + i \sin 200 ^ { \circ } \right) } { 4 \left( \cos 50 ^ { \circ } + i \sin 50 ^ { \circ } \right) }$