Trigonometry

Free Version

Upgrade subject to access all content

Moderate

Complex Numbers, DeMoivre’s Theorem, Standard Form

TRIG-YEZLFB

Given the complex number:

$$ z=2\left[ \cos { \left( \cfrac { \pi }{ 10 } \right) } +i\sin { \left( \cfrac { \pi }{ 10 } \right) } \right]$$

What is $ { z }^{ 5 }$ in standard form?

A

$ { z }^{ 5 }=2i$

B

$ { z }^{ 5 }=10i$

C

$ { z }^{ 5 }=32i$

D

$ { z }^{ 5 }=-32i$