How do you use DeMoivre's Theorem to simplify ${(2 (cos 10 + i sin 10))}^{8}$ $(2(cos10+isin10))^8$ ?

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Answer 1 · 2017-03-02T23:08:54

See below :)

${(2 (cos 10 + i sin 10))}^{8}$ $(2(cos10+isin10))^8$

$= 2^{8} {(cos 10 + i sin 10)}^{8}$ $= 2^8(cos10+isin10)^8$

$= 2^{8} (cos 80 + i sin 80)$ $= 2^8(cos80+isin80)$

That's as far as it goes

How do you use DeMoivre's Theorem to simplify (2(cos10+isin10))8(2(cos10+isin10))^8?