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Trigonometry

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Complex Natural Number, De Moivre’s Theorem, Rectangular Form

TRIG-9DUPJH

What is ${z_1} = 2{e^{i\frac{{5\pi }}{3}}}$ raised to the 5th power? (Give your answer in rectangular coordinate form rounded to the nearest thousandth)

A

$27.713 + 16i$

B

$16 + 27.713i$

C

$-16 - 27.713i$

D

$-27.713 - 16i $