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

Multiple Choice

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) $- \frac { 1 } { 2 } + \frac { \sqrt { 3 } } { 2 } \mathrm { i }$
B) $- 10 + 10 \sqrt { 3 } \mathrm { i }$
C) $- \frac { 5 \sqrt { 3 } } { 8 } + \frac { 5 } { 8 } \mathrm { i }$
D) $- 2 + 2 \sqrt { 3 } \mathrm { i }$