Multiply the complex numbers below and leave the result in trigonometric form. $\left[ 0.1 \left( \cos 260 ^ { \circ } + i \sin 260 ^ { \circ } \right) \right] \left[ 0.9 \left( \cos 220 ^ { \circ } + i \sin 220 ^ { \circ } \right) \right]$
A) $0.09 \left( \cos 120 ^ { \circ } + i \sin 120 ^ { \circ } \right)$
B) $0.09 \left( \cos 120 ^ { \circ } + i \sin 40 ^ { \circ } \right)$
C) $\cos 40 ^ { \circ } + i \sin 40 ^ { \circ }$
D) $0.09 \left( \cos 40 ^ { \circ } + i \sin 40 ^ { \circ } \right)$
E) $\cos 120 ^ { \circ } + i \sin 120 ^ { \circ }$

Question

Multiply the complex numbers below and leave the result in trigonometric form. $\left[ 0.1 \left( \cos 260 ^ { \circ } + i \sin 260 ^ { \circ } \right) \right] \left[ 0.9 \left( \cos 220 ^ { \circ } + i \sin 220 ^ { \circ } \right) \right]$  
A) $0.09 \left( \cos 120 ^ { \circ } + i \sin 120 ^ { \circ } \right)$
B)  $0.09 \left( \cos 120 ^ { \circ } + i \sin 40 ^ { \circ } \right)$
C)  $\cos 40 ^ { \circ } + i \sin 40 ^ { \circ }$
D)  $0.09 \left( \cos 40 ^ { \circ } + i \sin 40 ^ { \circ } \right)$
E)  $\cos 120 ^ { \circ } + i \sin 120 ^ { \circ }$

Quizplus · Accepted Answer

When multiplying complex numbers in trigonometric form, $r_1(\cos \theta_1 + i\sin \theta_1) \cdot r_2(\cos \theta_2 + i\sin \theta_2) = r_1r_2(\cos(\theta_1 + \theta_2) + i\sin(\theta_1 + \theta_2))$. Here, $0.1 \cdot 0.9 = 0.09$ and $260^\circ + 220^\circ = 480^\circ$, which is equivalent to $480^\circ - 360^\circ = 120^\circ$.

Multiply the Complex Numbers Below and Leave the Result in Trigonometric