Answer:
B
Step-by-step explanation:
[tex] \cos( \alpha ) + i\sin( \alpha ) = {e}^{i (\alpha + 2\pi)} [/tex]
z = 3(cos π/2 + i sin π/2) =→
[tex]3 {e}^{i \frac{\pi}{2} } [/tex]
z⁷ =
[tex] {3}^{7} {e}^{i \frac{7\pi}{2} } = {3}^{7} {e}^{i \frac{(7 - 4)\pi}{2} } = {3}^{7} {e}^{i \frac{3\pi}{2} } = {3}^{7} ( \cos( \frac{3\pi}{2} ) + i \sin( \frac{3\pi}{2} ) ) = 2187( \cos( \frac{3\pi}{2} ) + i \sin( \frac{3\pi}{2} ) )[/tex]
