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Trigonometry

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Complex Number, Square Root, All Roots

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TRIG-2U17BN

Given the complex number $ z=-\sqrt { 2 } +\sqrt { 2 } i$,

Find all the roots of $ \sqrt [ 3 ]{ z }$. If necessary, round your final answer to the nearest ten thousandths.

A

$0.8909+0.8909i,\; 1.2170+0.3261i,\; 0.3261+1.2170i$

B

$0.8909+0.8909i,\; -1.2170+0.3261i,\; 0.3261-1.2170i$

C

$-0.8909-0.8909i,\; -1.2170-0.3261i,\; -0.3261-1.2170i$

D

$0.8909-0.8909i,\; -1.2170-0.3261i,\; 0.3261+1.2170i$