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 the moduli and subtracting the angles. Here, the modulus of the numerator is 17 and the modulus of the denominator is 21, so the modulus of the result is $17/21$. The angle of the result is the difference of the angles, $59^\circ - 12^\circ = 47^\circ$. Therefore, the correct answer is $\frac{17}{21}(\cos 47^\circ + i\sin 47^\circ)$.