How do you use DeMoivre's Theorem to simplify ${(3 (cos 15 + i sin 15))}^{4}$ $(3(cos15+isin15))^4$ ?

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Answer 1 · 2018-03-02T05:49:22

$\frac{81}{2} (1 + i \sqrt{3})$ $81/2(1+isqrt3)$ .

De Moivre's Theorem states that,

${r (cos θ + i sin θ)}^{n} = r^{n} (cos n θ + i sin n θ)$ ${r(costheta+isintheta)}^n=r^n(cosntheta+isinntheta)$ .

$:. {3(cos15^@+isin15^@)}^4$ ,

$=3^4{cos(4xx15^@)+isin(4xx15^@)}$ ,

$=81(cos60^@+isin60^@)$ ,

$=81(1/2+isqrt3/2)$ ,

$=81/2(1+isqrt3)$ .

How do you use DeMoivre's Theorem to simplify (3(cos15+isin15))^4(3(cos15+isin15))4(3(cos15+isin15))^4?