Find Quotients of Complex Numbers in Polar Form
-$$\begin{array} { l }
z 1 = 8 \left( \cos 33 ^ { \circ } + i \sin 33 ^ { \circ } \right) \
z _ { 2 } = 2 \left( \cos 12 ^ { \circ } + i \sin 12 ^ { \circ } \right)
\end{array}$$
A) $4 \left( \cos 21 ^ { \circ } + i \sin 21 ^ { \circ } \right)$
B) $4 \left( \cos 45 ^ { \circ } + i \sin 45 ^ { \circ } \right)$
C) $6 \left( \cos \frac { 11 } { 4 } \circ + i \sin \frac { 11 } { 4 } \circ \right)$
D) $6 \left( \cos 21 ^ { \circ } - i \sin 21 ^ { \circ } \right)$

Question

Find Quotients of Complex Numbers in Polar Form
-$$\begin{array} { l } 
z 1 = 8 \left( \cos 33 ^ { \circ } + i \sin 33 ^ { \circ } \right) \
z _ { 2 } = 2 \left( \cos 12 ^ { \circ } + i \sin 12 ^ { \circ } \right)
\end{array}$$
A) $4 \left( \cos 21 ^ { \circ } + i \sin 21 ^ { \circ } \right)$
B) $4 \left( \cos 45 ^ { \circ } + i \sin 45 ^ { \circ } \right)$
C) $6 \left( \cos \frac { 11 } { 4 } \circ + i \sin \frac { 11 } { 4 } \circ \right)$
D) $6 \left( \cos 21 ^ { \circ } - i \sin 21 ^ { \circ } \right)$

Quizplus · Accepted Answer

To divide two complex numbers in polar form, you divide their magnitudes and subtract their angles. For $z_1$ and $z_2$, the quotient's magnitude is $8/2 = 4$ and the angle is $33^\circ - 12^\circ = 21^\circ$, resulting in $4(\cos 21^\circ + i\sin 21^\circ)$.

Find Quotients of Complex Numbers in Polar Form - A) 4(cos⁡21∘+isin⁡21∘)4 \left( \cos 21 ^ { \circ } + i \sin 21 ^ { \circ } \right)4(cos21∘+isin21∘)

Find Quotients of Complex Numbers in Polar Form
- A) $4 \left( \cos 21 ^ { \circ } + i \sin 21 ^ { \circ } \right)$