How do you use DeMoivre's theorem to simplify ${(2 e^{30 i})}^{3}$ $(2e^(30i))^3$ ?

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Answer 1 · 2017-07-13T13:49:46

$8 [cos (90 - 28 π) + i sin (90 - 28 π)]$ $8[cos (90 - 28 pi) + i sin (90 - 28 pi)]$

$e^{i t} = cos t + i sin t$ $e^(it) = cos t + i sin t$

$X = 2^{3} {(cos 30 + i sin 30)}^{3}$ $X = 2^3(cos 30 + i sin 30)^3$

$= 8 (cos 90 + i sin 90)$ $= 8(cos 90 + i sin 90)$

$14 * 2pi = 87,9645943...$

How do you use DeMoivre's theorem to simplify (2e^(30i))^3(2e30i)3(2e^(30i))^3?