Perform the operation below and leave the result in trigonometric form. $$\frac { 4 \left( \cos 58 ^ { \circ } + i \sin 58 ^ { \circ } \right) } { 12 \left( \cos 13 ^ { \circ } + i \sin 13 ^ { \circ } \right) }$$
A) $\frac { 1 } { 3 } \left( \cos 45 ^ { \circ } + i \sin 45 ^ { \circ } \right)$
B) $- 8 \left( \cos \frac { 58 ^ { \circ } } { 13 } + i \sin \frac { 58 ^ { \circ } } { 13 } \right)$
C) $16 \left( \cos 71 ^ { \circ } + i \sin 71 ^ { \circ } \right)$
D) $48 \left( \cos \frac { 58 ^ { \circ } } { 13 } + i \sin \frac { 58 ^ { \circ } } { 13 } \right)$
E) $\frac { 1 } { 3 } \left( \cos \frac { 58 ^ { \circ } } { 13 } + i \sin \frac { 58 ^ { \circ } } { 13 } \right)$

Question

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 $4/12 = 1/3$ and the angles subtract to give $58^\circ - 13^\circ = 45^\circ$, resulting in $\frac{1}{3}(\cos 45^\circ + i\sin 45^\circ)$.