?

Trigonometry

Free Version

Upgrade subject to access all content

Difficult

Complex Numbers, Rational Exponent, Trigonometric Form

TRIG-WALJRP

Given $z=6+9i$,

Find the primary value of ${ z }^{ \frac{ 2 }{ 3 } }$ in trigonometric form.

A

${ \left( \sqrt { 117 } \right) }^{ { 7 }/{ 6 } }\left( \cos { \left( 0.655 \right) } +i\sin { \left( 0.655 \right) } \right)$

B

$ \sqrt [ 3 ]{ 117 } \left( \cos { \left( 0.392 \right) } +i\sin { \left( 0.392 \right) } \right)$

C

$ \sqrt [ 3 ]{ 117 } \left( \cos { \left( 0.655 \right) } +i\sin { \left( 0.655 \right) } \right)$

D

${ \left( \sqrt { 117 } \right) }^{ { 7 }/{ 6 } }\left( \cos { \left( 0.392 \right) } +i\sin { \left( 0.392 \right) } \right)$