?

Trigonometry

Free Version

Upgrade subject to access all content

Easy

Complex Number, DeMoivre’s Theorem, Power of a Number, Trig Form

TRIG-VL7Y99

Given the complex number $ z=6\left[ \cos { \left( \cfrac { \pi }{ 2 } \right) } +i\sin { \left( \cfrac { \pi }{ 2 } \right) } \right]$,

What is $ { z }^{ 3 }$ in trigonometric form?

A

${ z }^{ 3 }={ 216\left[ \cos { \left( \cfrac { \pi }{ 2 } \right) } +i\sin { \left( \cfrac { \pi }{ 2 } \right) } \right] }$

B

${ z }^{ 3 }={ 18\left[ \cos { \left( \cfrac { 3\pi }{ 2 } \right) } +i\sin { \left( \cfrac { 3\pi }{ 2 } \right) } \right] }$

C

${ z }^{ 3 }={ 18\left[ \cos { \left( \cfrac { \pi }{ 2 } \right) } +i\sin { \left( \cfrac { \pi }{ 2 } \right) } \right] }$

D

${ z }^{ 3 }={ 216\left[ \cos { \left( \cfrac { 3\pi }{ 2 } \right) } +i\sin { \left( \cfrac { 3\pi }{ 2 } \right) } \right] }$