Question

Express (sin 30 + i cos 30)^18​

Answer 1

-i.

Explanation:

Applying DeMoivre' s theorem:

(sin 30 + i cos 30)^18​

= sin(18*30) + i cos(18*30)

= sin 540 + i cos 540

= sin (3*180) + i cos (3*180)

= 0 + -1 * i

= -i.