Find the product or quotient, as indicated. Leave your answer in polar form.
-Find the product of $\mathrm { z } _ { 1 }$ and $\mathrm { z } _ { 2 }$.
$\mathrm { z } _ { 1 } = 8 \left( \cos 35 ^ { \circ } + \mathrm { i } \sin 35 ^ { \circ } \right) , \mathrm { z } _ { 2 } = 4 \left( \cos 125 ^ { \circ } + \mathrm { i } \sin 125 ^ { \circ } \right)$
A) $32 \left( \cos 4375 ^ { \circ } + i \sin 4375 ^ { \circ } \right)$
B) $12 \left( \cos 160 ^ { \circ } + i \sin 160 ^ { \circ } \right)$
C) $32 \left( \cos 160 ^ { \circ } + i \sin 160 ^ { \circ } \right)$
D) $32 \left( \cos 35 ^ { \circ } + i \sin 35 ^ { \circ } \right)$

Question

Quizplus · Accepted Answer

To find the product of two complex numbers in polar form, you multiply their magnitudes and add their angles. Here, the magnitudes are 8 and 4, so their product is 32. The angles are 35° and 125°, so their sum is 160°. Therefore, the product in polar form is $32(\cos 160^\circ + i\sin 160^\circ)$.

Find the Product or Quotient, as Indicated z1\mathrm { z } _ { 1 }z1​

Find the Product or Quotient, as Indicated $\mathrm { z } _ { 1 }$