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 the magnitudes and subtracting the angles. Here, the magnitudes are 5 and 4, and the angles are 4.5 degrees and 2.4 degrees. Thus, the result is $\frac{5}{4}(\cos(4.5^\circ - 2.4^\circ) + i\sin(4.5^\circ - 2.4^\circ)) = \frac{5}{4}(\cos 2.1^\circ + i\sin 2.1^\circ)$.