Question

PLEASE PLEASE HELP!!!!

Answer 1

B

Explanation:

`\cos( \alpha ) + i\sin( \alpha ) = {e}^(i (\alpha + 2\pi))`

z = 3(cos π/2 + i sin π/2) =→

`3 {e}^{i (\pi)/(2) }`

z⁷ =

`{3}^(7) {e}^{i (7\pi)/(2) } = {3}^(7) {e}^{i ((7 - 4)\pi)/(2) } = {3}^(7) {e}^{i (3\pi)/(2) } = {3}^(7) ( \cos( (3\pi)/(2) ) + i \sin( (3\pi)/(2) ) ) = 2187( \cos( (3\pi)/(2) ) + i \sin( (3\pi)/(2) ) )`