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

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Answer 1 · 2018-03-02T05:49:22

# 81/2(1+isqrt3)#.

De Moivre's Theorem states that,

#{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)#.