Find (Z1)(Z2) Leave answer in polar form

**Given:**

Z1= sqrt.6(cos(5pi/6) + i sin(5pi/6))

Z2= sqrt.2(cos(5pi/4) + i sin (5pi/4))

__Find (Z1)(Z2) Leave answer in polar form__

This is what i got so far and i don't know if i started right.

=sqrt.12(cos(5pi/6) + i sin(5pie/6)) (cos(5pi/4) + i sin(5pi/4))

=sqrt.12(cos(5pi/4) + cos(5pie/6) i sin(5pi/4) + i sin(5pi/6) cos(5pi/4) - i sin(5pi/6) sin(5pi/4))

and i don't know if its right and don't know how to finish it, and if you can, can you show step by step if possible.