Perform the operation and leave the result in trigonometric form. $\frac { 5 \left( \cos 4.5 ^ { \circ } + i \sin 4.5 ^ { \circ } \right) } { 4 \left( \cos 2.4 ^ { \circ } + i \sin 2.4 ^ { \circ } \right) }$
A) $\frac { 5 } { 4 } \left( \cos 4.5 ^ { \circ } + i \sin 4.5 ^ { \circ } \right)$
B) $\frac { 5 } { 4 } \left( \cos 2.1 ^ { \circ } - i \sin 2.1 ^ { \circ } \right)$
C) $\frac { 5 } { 4 } \left( \cos 2.1 ^ { \circ } + i \sin 2.1 ^ { \circ } \right)$
D) $\frac { 5 } { 4 } \left( \cos 4.5 ^ { \circ } - i \sin 4.5 ^ { \circ } \right)$
E) $\frac { 5 } { 4 } \left( \cos 2.4 ^ { \circ } + i \sin 2.4 ^ { \circ } \right)$

Question

Perform the operation and leave the result in trigonometric form.   $\frac { 5 \left( \cos 4.5 ^ { \circ } + i \sin 4.5 ^ { \circ } \right) } { 4 \left( \cos 2.4 ^ { \circ } + i \sin 2.4 ^ { \circ } \right) }$  
A) $\frac { 5 } { 4 } \left( \cos 4.5 ^ { \circ } + i \sin 4.5 ^ { \circ } \right)$
B)  $\frac { 5 } { 4 } \left( \cos 2.1 ^ { \circ } - i \sin 2.1 ^ { \circ } \right)$
C)  $\frac { 5 } { 4 } \left( \cos 2.1 ^ { \circ } + i \sin 2.1 ^ { \circ } \right)$
D)  $\frac { 5 } { 4 } \left( \cos 4.5 ^ { \circ } - i \sin 4.5 ^ { \circ } \right)$
E)  $\frac { 5 } { 4 } \left( \cos 2.4 ^ { \circ } + i \sin 2.4 ^ { \circ } \right)$

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 $5/4$ and the angle difference is $4.5^\circ - 2.4^\circ = 2.1^\circ$, resulting in $\frac{5}{4}(\cos 2.1^\circ + i\sin 2.1^\circ)$.