4(1-sqrt3i)^3
Let z=(1-sqrt3i)^3
r=sqrt[(1)^2+(-sqrt3)^2]=sqrt[1+3]=sqrt4=2
theta=arctan(-sqrt3/1)=arctan(-sqrt3)=(5pi)/3
DeMoivre's Theorem
z^n=[r(costheta+isintheta)]^n=r^n[cosntheta+isinntheta]
z^3=[2(cos(5pi)/3+isin(5pi)/3]^3=(2)^3[cos3((5pi)/3)+isin3((5pi)/3)]
z^3=8[cos(5pi)+isin(5pi)
z^3=8[-1+0i]
z^3=-8
4z^3=4(-8)=-32
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