How do you use DeMoivre's Theorem to simplify #(5(cos20+isin20))^3#?

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Answer 1 · 2016-11-19T17:42:14

The answer is #=125/2(1+isqrt3)#

DeMoivre 'theorem is

#(costheta+isintheta)^n= cosntheta+isinntheta#

Therefore,

#(5(cos20+isin20))^3#

#=5^3(cos3*20+isin3*20)#

#=125 (cos60+isin60)#

#=125(1/2+isqrt3/2)#