Find the product or quotient, as indicated. Leave your answer in polar form.
-Find the product of $z _ { 1 }$ and $z _ { 2 }$.
$$z _ { 1 } = 5 \left[ \cos \left( 75 ^ { \circ } \right) + i \sin \left( 75 ^ { \circ } \right) \right] , z _ { 2 } = \sqrt { 3 } \left( \cos - 135 ^ { \circ } + i \sin - 135 ^ { \circ } \right)$$
A) $5 \sqrt { 3 } \left[ \cos \left( 210 ^ { \circ } \right) + i \sin \left( 210 ^ { \circ } \right) \right]$
B) $( 5 + \sqrt { 3 } ) \left[ \cos \left( - 60 ^ { \circ } \right) + i \sin \left( - 60 ^ { \circ } \right) \right]$
C) $5 \sqrt { 3 } \left[ \cos \left( - 60 ^ { \circ } \right) + \mathrm { i } \sin \left( - 60 ^ { \circ } \right) \right]$
D) $5 \sqrt { 3 } \left[ \cos \left( - 10,125 ^ { \circ } \right) + i \sin \left( - 10,125 ^ { \circ } \right) \right]$

Question

Quizplus · Accepted Answer

To find the product of two complex numbers in polar form, multiply their magnitudes and add their angles. The magnitude is $5 \times \sqrt{3} = 5\sqrt{3}$. The angle is $75^\circ + (-135^\circ) = -60^\circ$. Thus, the product is $5\sqrt{3} \left[ \cos(-60^\circ) + i \sin(-60^\circ) \right]$.

Find the Product or Quotient, as Indicated z1z _ { 1 }z1​

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