Solve the problem. Leave your answer in polar form.
-$$\begin{array} { l }
z = 10 \left( \cos 30 ^ { \circ } + i \sin 30 ^ { \circ } \right) \
w = 5 \left( \cos 10 ^ { \circ } + i \sin 10 ^ { \circ } \right)
\end{array}$$
Find zw.
A) $50 \left( \cos 40 ^ { \circ } + i \sin 40 ^ { \circ } \right)$
B) $15 \left( \cos 40 ^ { \circ } + i \sin 40 ^ { \circ } \right)$
C) $15 \left( \cos 300 ^ { \circ } + i \sin 300 ^ { \circ } \right)$
D) $50 \left( \cos 300 ^ { \circ } + \mathrm { i } \sin 300 ^ { \circ } \right)$

Question

Solve the problem. Leave your answer in polar form.
-$$\begin{array} { l } 
z = 10 \left( \cos 30 ^ { \circ } + i \sin 30 ^ { \circ } \right) \
w = 5 \left( \cos 10 ^ { \circ } + i \sin 10 ^ { \circ } \right)
\end{array}$$
Find zw.
A) $50 \left( \cos 40 ^ { \circ } + i \sin 40 ^ { \circ } \right)$
B) $15 \left( \cos 40 ^ { \circ } + i \sin 40 ^ { \circ } \right)$
C) $15 \left( \cos 300 ^ { \circ } + i \sin 300 ^ { \circ } \right)$
D) $50 \left( \cos 300 ^ { \circ } + \mathrm { i } \sin 300 ^ { \circ } \right)$

Quizplus · Accepted Answer

When multiplying two complex numbers in polar form, you multiply their magnitudes and add their angles. Thus, $zw = 10 \times 5 \left( \cos(30^\circ + 10^\circ) + i \sin(30^\circ + 10^\circ) \right) = 50 \left( \cos 40^\circ + i \sin 40^\circ \right)$.

Solve the Problem Find Zw A) 50(cos⁡40∘+isin⁡40∘)50 \left( \cos 40 ^ { \circ } + i \sin 40 ^ { \circ } \right)50(cos40∘+isin40∘)

Solve the Problem Find Zw
A) $50 \left( \cos 40 ^ { \circ } + i \sin 40 ^ { \circ } \right)$