Find Products of Complex Numbers in Polar Form
-$$\begin{array} { l }
\mathrm { z } 1 = 3 \left( \cos 34 ^ { \circ } + \mathrm { i } \sin 34 ^ { \circ } \right) \
\mathrm { z } 2 = 7 \left( \cos 8 ^ { \circ } + \mathrm { i } \sin 8 ^ { \circ } \right)
\end{array}$$
A) $21 \left( \cos 42 ^ { \circ } + i \sin 42 ^ { \circ } \right)$
B) $21 \left( \cos 26 ^ { \circ } + i \sin 26 ^ { \circ } \right)$
C) $10 \left( \cos 42 ^ { \circ } + i \sin 42 ^ { \circ } \right)$
D) $10 \left( \cos 272 ^ { \circ } + i \sin 272 ^ { \circ } \right)$

Question

Find Products of Complex Numbers in Polar Form
-$$\begin{array} { l } 
\mathrm { z } 1 = 3 \left( \cos 34 ^ { \circ } + \mathrm { i } \sin 34 ^ { \circ } \right) \
\mathrm { z } 2 = 7 \left( \cos 8 ^ { \circ } + \mathrm { i } \sin 8 ^ { \circ } \right)
\end{array}$$
A) $21 \left( \cos 42 ^ { \circ } + i \sin 42 ^ { \circ } \right)$
B) $21 \left( \cos 26 ^ { \circ } + i \sin 26 ^ { \circ } \right)$
C) $10 \left( \cos 42 ^ { \circ } + i \sin 42 ^ { \circ } \right)$
D) $10 \left( \cos 272 ^ { \circ } + i \sin 272 ^ { \circ } \right)$

Quizplus · Accepted Answer

The product of two complex numbers in polar form is obtained by multiplying their magnitudes and adding their angles. Here, $3 \times 7 = 21$ and $34^\circ + 8^\circ = 42^\circ$, resulting in $21(\cos 42^\circ + i\sin 42^\circ)$.

Find Products of Complex Numbers in Polar Form - A) 21(cos⁡42∘+isin⁡42∘)21 \left( \cos 42 ^ { \circ } + i \sin 42 ^ { \circ } \right)21(cos42∘+isin42∘)

Find Products of Complex Numbers in Polar Form
- A) $21 \left( \cos 42 ^ { \circ } + i \sin 42 ^ { \circ } \right)$