Perform the operation below and leave the result in trigonometric form.
$$\frac { 17 \left( \cos 59 ^ { \circ } + i \sin 59 ^ { \circ } \right) } { 21 \left( \cos 12 ^ { \circ } + i \sin 12 ^ { \circ } \right) }$$
A) $\frac { 17 } { 21 } \left( \cos 47 ^ { \circ } + i \sin 47 ^ { \circ } \right)$
B) $- 4 \left( \cos \frac { 59 ^ { \circ } } { 12 } + i \sin \frac { 59 ^ { \circ } } { 12 } \right)$
C) $38 \left( \cos 71 ^ { \circ } + i \sin 71 ^ { \circ } \right)$
D) $357 \left( \cos \frac { 59 ^ { \circ } } { 12 } + i \sin \frac { 59 ^ { \circ } } { 12 } \right)$
E) $\frac { 17 } { 21 } \left( \cos \frac { 59 ^ { \circ } } { 12 } + i \sin \frac { 59 ^ { \circ } } { 12 } \right)$

Question

Quizplus · Accepted Answer

The division of complex numbers in trigonometric form is performed by dividing their magnitudes and subtracting their angles. Thus, the magnitude is $17/21$ and the angle is $59^\circ - 12^\circ = 47^\circ$, resulting in $\frac{17}{21}(\cos 47^\circ + i\sin 47^\circ)$.