Question #4d92c

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Answer 1 · 2017-04-05T21:22:36

$= 2 (1 + j sqrt3), -4 , 2(1 - j sqrt3)$

$(64(cos(pi)+jsin(pi)))^(1/3)$

$= 64^(1/3) (cis(pi + 2n pi))^(1/3)$

$= 4 (e^(j \ (pi + 2n pi)))^(1/3)$

$= 4 e^(j (pi+ 2n pi)/3)$

Working through the $n$ 's:

$= 4 e^(j (pi)/3), 4 e^(j pi), 4 e^(j (5 pi)/3)$

They start repeating after that.

$= 4 \ cis ((pi)/3), 4 \ cis ( pi), 4 \ cis (5 pi)/3$

$= 2 (1 + j sqrt3), -4 , 2(1 - j sqrt3)$