Question #22412

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Answer 1 · 2017-12-10T10:32:06

# 81(cos600^@+isin600^@)=-(81/2+i(81sqrt3)/2).#

By De'Moivre's Theorem,

#{r(costheta+isintheta)}^n=r^n{cos(ntheta)+isin(ntheta)}.#

In our Problem, #r=3, theta=150^@, and n=4.#

#:. {3cos150^@+isin150^@}^4,#

#=3^4{cos(4*150^@)=isin(4*150^@)},#

#=81(cos600^@+isin600^@),#

#=81{cos(3*180^@+60^@)+isin(3*180^@+60^@)},#

#=81(-cos60^@-isin60^@),#

#=81(-1/2-isqrt3/2),#

#=-(81/2+i(81sqrt3)/2).#