How do you use DeMoivre's Theorem to simplify $(5(cos3.2+isin3.2))^4$ ?

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Answer 1 · 2016-09-30T10:12:04

$(5(cos3.2+isin3.2))^4=625(cos12.8+isin12.8)$

DeMoivre's Theorem states that if we have a complex number

$z=r(costheta+isintheta)$ , then

$z^n=r^n(cosntheta+isinntheta)$

Hence $(5(cos3.2+isin3.2))^4$

= $5^4(cos(3.2xx4)+isin(3.2xx4))$

= $625(cos12.8+isin12.8)$

How do you use DeMoivre's Theorem to simplify (5(cos3.2+isin3.2))^4(5(cos3.2+isin3.2))^4?