Question

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

Answer 1

The answer is D hope this helps

Answer 2

Answer:

$D)\displaystyle \rm \frac{ \sqrt{3} }{12} cis \left( \frac{19\pi}{15} \right)$

Step-by-step explanation:

remember that

$\displaystyle a \rm cis( \theta) \times b cis( \theta _{2}) = ab \cdot cis( \theta + \theta _{2})$

so we acquire:

$\displaystyle \frac{ \sqrt{2} }{6} \rm cis \left( \frac{3\pi}{5} \right) \times \frac{ \sqrt{6} }{4} cis \left( \frac{2\pi}{3} \right) = \frac{ \sqrt{2} }{6} \times \frac{ \sqrt{6} }{4} \cdot cis \left( \frac{3\pi}{5} + \frac{2\pi}{3} \right)$

simplify the left hand side

$\displaystyle \rm \frac{ \sqrt{12} }{24} \cdot cis \left( \frac{3\pi}{5} + \frac{2\pi}{3} \right)$

$\displaystyle \rm \frac{2 \sqrt{3} }{24} \cdot cis \left( \frac{3\pi}{5} + \frac{2\pi}{3} \right)$

reduce fraction:

$\displaystyle \rm \frac{ \sqrt{3} }{12} \cdot cis \left( \frac{3\pi}{5} + \frac{2\pi}{3} \right)$

simplify addition:

$\displaystyle \rm \frac{ \sqrt{3} }{12} cis \left( \frac{19\pi}{15} \right)$

hence our answer is D