Find Products of Complex Numbers in Polar Form
-$$\begin{array} { l }
z 1 = 5 \left( \cos 20 ^ { \circ } + i \sin 20 ^ { \circ } \right) \
z 2 = 4 \left( \cos 10 ^ { \circ } + i \sin 10 ^ { \circ } \right)
\end{array}$$
A) $20 \left( \cos 30 ^ { \circ } + i \sin 30 ^ { \circ } \right)$
B) $20 \left( \cos 200 ^ { \circ } + i \sin 200 ^ { \circ } \right)$
C) $9 \left( \cos 30 ^ { \circ } + i \sin 30 ^ { \circ } \right)$
D) $9 \left( - \cos 200 ^ { \circ } - i \sin 200 ^ { \circ } \right)$

Question

Find Products of Complex Numbers in Polar Form
-$$\begin{array} { l } 
z 1 = 5 \left( \cos 20 ^ { \circ } + i \sin 20 ^ { \circ } \right) \
z 2 = 4 \left( \cos 10 ^ { \circ } + i \sin 10 ^ { \circ } \right)
\end{array}$$
A) $20 \left( \cos 30 ^ { \circ } + i \sin 30 ^ { \circ } \right)$
B) $20 \left( \cos 200 ^ { \circ } + i \sin 200 ^ { \circ } \right)$
C) $9 \left( \cos 30 ^ { \circ } + i \sin 30 ^ { \circ } \right)$
D) $9 \left( - \cos 200 ^ { \circ } - i \sin 200 ^ { \circ } \right)$

Quizplus · Accepted Answer

The product of two complex numbers in polar form is obtained by multiplying their magnitudes and adding their angles. Here, $|z_1| = 5$, $|z_2| = 4$, $\theta_1 = 20^\circ$, and $\theta_2 = 10^\circ$. Thus, $|z_1z_2| = 5 \times 4 = 20$ and $\theta_{total} = 20^\circ + 10^\circ = 30^\circ$, resulting in $20(\cos 30^\circ + i\sin 30^\circ)$.

Find Products of Complex Numbers in Polar Form - A) 20(cos⁡30∘+isin⁡30∘)20 \left( \cos 30 ^ { \circ } + i \sin 30 ^ { \circ } \right)20(cos30∘+isin30∘)

Find Products of Complex Numbers in Polar Form
- A) $20 \left( \cos 30 ^ { \circ } + i \sin 30 ^ { \circ } \right)$