Question

Besties can any of you help me on this because i do not know how to solve this

90 points for correct answers only

Answer 1

The answer is D hope this helps

Answer 2

`D)\displaystyle \rm ( √(3) )/(12) cis \left( (19\pi)/(15) \right)`

Explanation:

remember that

`\displaystyle a \rm cis( \theta) * b cis( \theta _(2)) = ab \cdot cis( \theta + \theta _(2))`

so we acquire:

`\displaystyle ( √(2) )/(6) \rm cis \left( (3\pi)/(5) \right) * ( √(6) )/(4) cis \left( (2\pi)/(3) \right) = ( √(2) )/(6) * ( √(6) )/(4) \cdot cis \left( (3\pi)/(5) + (2\pi)/(3) \right)`

simplify the left hand side

`\displaystyle \rm ( √(12) )/(24) \cdot cis \left( (3\pi)/(5) + (2\pi)/(3) \right)`

`\displaystyle \rm (2 √(3) )/(24) \cdot cis \left( (3\pi)/(5) + (2\pi)/(3) \right)`

reduce fraction:

`\displaystyle \rm ( √(3) )/(12) \cdot cis \left( (3\pi)/(5) + (2\pi)/(3) \right)`

simplify addition:

`\displaystyle \rm ( √(3) )/(12) cis \left( (19\pi)/(15) \right)`

hence our answer is D