Divide the complex numbers below and leave the result in trigonometric form. $\frac { 10 \left( \cos 220 ^ { \circ } + i \sin 220 ^ { \circ } \right) } { 7 \left( \cos 210 ^ { \circ } + i \sin 210 ^ { \circ } \right) }$
A) $70 \left( \cos 10 ^ { \circ } + i \sin 10 ^ { \circ } \right)$
B) $\frac { 10 } { 7 } \left( \cos 10 ^ { \circ } + i \sin 70 ^ { \circ } \right)$
C) $\frac { 10 } { 7 } \left( \cos 70 ^ { \circ } + i \sin 70 ^ { \circ } \right)$
D) $\frac { 10 } { 7 } \left( \cos 10 ^ { \circ } + i \sin 10 ^ { \circ } \right)$
E) $70 \left( \cos 70 ^ { \circ } + i \sin 70 ^ { \circ } \right)$

Question

Divide the complex numbers below and leave the result in trigonometric form. $\frac { 10 \left( \cos 220 ^ { \circ } + i \sin 220 ^ { \circ } \right) } { 7 \left( \cos 210 ^ { \circ } + i \sin 210 ^ { \circ } \right) }$
A) $70 \left( \cos 10 ^ { \circ } + i \sin 10 ^ { \circ } \right)$
B)  $\frac { 10 } { 7 } \left( \cos 10 ^ { \circ } + i \sin 70 ^ { \circ } \right)$
C)  $\frac { 10 } { 7 } \left( \cos 70 ^ { \circ } + i \sin 70 ^ { \circ } \right)$
D)  $\frac { 10 } { 7 } \left( \cos 10 ^ { \circ } + i \sin 10 ^ { \circ } \right)$
E)  $70 \left( \cos 70 ^ { \circ } + i \sin 70 ^ { \circ } \right)$

Quizplus · Accepted Answer

When dividing complex numbers in trigonometric form, the magnitudes divide and the angles subtract. Thus, the result is $\frac{10}{7} \left( \cos(220^\circ - 210^\circ) + i \sin(220^\circ - 210^\circ) \right) = \frac{10}{7} \left( \cos 10^\circ + i \sin 10^\circ \right)$.

Divide the Complex Numbers Below and Leave the Result in Trigonometric