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Trigonometry

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Complex, Numbers, DeMoivre’s Theorem, Powers of Complex Number

TRIG-21UBIU

Given ${ z }_{ 1 }=2\left[ \cos { \left( \cfrac { 3\pi }{ 4 } \right) } +i\sin { \left( \cfrac { 3\pi }{ 4 } \right) } \right] $,

Find ${ \left( { z }_{ 1 } \right) }^{ 5 }$, and convert your answer to standard form.

A

$-16\sqrt { 2 } -16\sqrt { 2 } i$

B

$16\sqrt { 2 } -16\sqrt { 2 } i$

C

$31.325928 +6.53347 i$

D

$\sqrt { 2 } -\sqrt { 2 } i$