Perform the operation and leave the result in trigonometric form. $$\frac { 2 \left( \cos 30 ^ { \circ } + i \sin 30 ^ { \circ } \right) } { 3 \left( \cos 120 ^ { \circ } + i \sin 120 ^ { \circ } \right) }$$
A) $\frac { 2 } { 3 } \left( \cos 270 ^ { \circ } + i \sin 270 ^ { \circ } \right)$
B) $\frac { 2 } { 3 } \left( \cos 30 ^ { \circ } + i \sin 30 ^ { \circ } \right)$
C) $\frac { 2 } { 3 } \left( \cos 270 ^ { \circ } - i \sin 270 ^ { \circ } \right)$
D) $\frac { 2 } { 3 } \left( \cos 30 ^ { \circ } - i \sin 30 ^ { \circ } \right)$
E) $\frac { 2 } { 3 } \left( \cos 120 ^ { \circ } + i \sin 120 ^ { \circ } \right)$

Question

Perform the operation and leave the result in trigonometric form.​ $$\frac { 2 \left( \cos 30 ^ { \circ } + i \sin 30 ^ { \circ } \right) } { 3 \left( \cos 120 ^ { \circ } + i \sin 120 ^ { \circ } \right) }$$ ​
A) $\frac { 2 } { 3 } \left( \cos 270 ^ { \circ } + i \sin 270 ^ { \circ } \right)$
B)​ $\frac { 2 } { 3 } \left( \cos 30 ^ { \circ } + i \sin 30 ^ { \circ } \right)$
C)​ $\frac { 2 } { 3 } \left( \cos 270 ^ { \circ } - i \sin 270 ^ { \circ } \right)$
D)​ $\frac { 2 } { 3 } \left( \cos 30 ^ { \circ } - i \sin 30 ^ { \circ } \right)$
E)​ $\frac { 2 } { 3 } \left( \cos 120 ^ { \circ } + i \sin 120 ^ { \circ } \right)$

Quizplus · Accepted Answer

The division of complex numbers in trigonometric form is performed by dividing their magnitudes and subtracting their angles. Here, the magnitudes are 2/3 and the angles subtract to give 30° - 120° = -90°, which is equivalent to 270°.