Solve the problem. Leave your answer in polar form.
-$$\begin{array} { l }
z = 10 \left( \cos 45 ^ { \circ } + i \sin 45 ^ { \circ } \right) \
w = 5 \left( \cos 15 ^ { \circ } + i \sin 15 ^ { \circ } \right)
\end{array}$$
Find $z w$.
A) $5 \left( \cos 60 ^ { \circ } + i \sin 60 ^ { \circ } \right)$
B) $50 \left( \cos 60 ^ { \circ } + i \sin 60 ^ { \circ } \right)$
C) $50 \left( \cos 30 ^ { \circ } + \mathrm { i } \sin 30 ^ { \circ } \right)$
D) $5 \left( \cos 30 ^ { \circ } + i \sin 30 ^ { \circ } \right)$

Question

Solve the problem. Leave your answer in polar form.
-$$\begin{array} { l } 
z = 10 \left( \cos 45 ^ { \circ } + i \sin 45 ^ { \circ } \right) \
w = 5 \left( \cos 15 ^ { \circ } + i \sin 15 ^ { \circ } \right)
\end{array}$$
Find $z w$.
A) $5 \left( \cos 60 ^ { \circ } + i \sin 60 ^ { \circ } \right)$
B) $50 \left( \cos 60 ^ { \circ } + i \sin 60 ^ { \circ } \right)$
C) $50 \left( \cos 30 ^ { \circ } + \mathrm { i } \sin 30 ^ { \circ } \right)$
D) $5 \left( \cos 30 ^ { \circ } + i \sin 30 ^ { \circ } \right)$

Quizplus · Accepted Answer

To multiply two complex numbers in polar form, you multiply their magnitudes and add their angles. Here, $z = 10(\cos 45^\circ + i\sin 45^\circ)$ and $w = 5(\cos 15^\circ + i\sin 15^\circ)$. Multiplying their magnitudes gives $10 \times 5 = 50$, and adding their angles gives $45^\circ + 15^\circ = 60^\circ$. Therefore, $zw = 50(\cos 60^\circ + i\sin 60^\circ)$.

Solve the Problem Find zwz wzw A) 5(cos⁡60∘+isin⁡60∘)5 \left( \cos 60 ^ { \circ } + i \sin 60 ^ { \circ } \right)5(cos60∘+isin60∘)

Solve the Problem Find $z w$
A) $5 \left( \cos 60 ^ { \circ } + i \sin 60 ^ { \circ } \right)$