Divide the complex numbers below and leave the result in trigonometric form. $$\frac { 5 \left( \cos 100 ^ { \circ } + i \sin 100 ^ { \circ } \right) } { 9 \left( \cos 120 ^ { \circ } + i \sin 120 ^ { \circ } \right) }$$
A) $\frac { 5 } { 9 } \left( \cos 220 ^ { \circ } + i \sin 220 ^ { \circ } \right)$
B) $\frac { 5 } { 9 } \left( \cos 340 ^ { \circ } + i \sin 340 ^ { \circ } \right)$
C) $45 \left( \cos 220 ^ { \circ } + i \sin 220 ^ { \circ } \right)$
D) $\frac { 5 } { 9 } \left( \cos 340 ^ { \circ } + i \sin 220 ^ { \circ } \right)$
E) $45 \left( \cos 340 ^ { \circ } + i \sin 340 ^ { \circ } \right)$

Question

Divide the complex numbers below and leave the result in trigonometric form. $$\frac { 5 \left( \cos 100 ^ { \circ } + i \sin 100 ^ { \circ } \right) } { 9 \left( \cos 120 ^ { \circ } + i \sin 120 ^ { \circ } \right) }$$ ​
A) $\frac { 5 } { 9 } \left( \cos 220 ^ { \circ } + i \sin 220 ^ { \circ } \right)$
B)​ $\frac { 5 } { 9 } \left( \cos 340 ^ { \circ } + i \sin 340 ^ { \circ } \right)$
C)​ $45 \left( \cos 220 ^ { \circ } + i \sin 220 ^ { \circ } \right)$
D)​ $\frac { 5 } { 9 } \left( \cos 340 ^ { \circ } + i \sin 220 ^ { \circ } \right)$
E)​ $45 \left( \cos 340 ^ { \circ } + i \sin 340 ^ { \circ } \right)$

Quizplus · Accepted Answer

When dividing complex numbers in trigonometric form, you divide the magnitudes and subtract the angles. Here, the magnitude is $\frac{5}{9}$ and the angle difference is $100^\circ - 120^\circ = -20^\circ$, which is equivalent to $340^\circ$ (since $360^\circ - 20^\circ = 340^\circ$). Therefore, the correct answer is in the form $\frac{5}{9}(\cos 340^\circ + i\sin 340^\circ)$.

Divide the Complex Numbers Below and Leave the Result in Trigonometric