已知虚数z满足z^3=8,则z^3+z^2+2z+2=___________已知虚数z满足z^3=8,则z^3+z^2+2z+2=__________

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已知虚数z满足z^3=8,则z^3+z^2+2z+2=___________已知虚数z满足z^3=8,则z^3+z^2+2z+2=__________

已知虚数z满足z^3=8,则z^3+z^2+2z+2=___________已知虚数z满足z^3=8,则z^3+z^2+2z+2=__________
已知虚数z满足z^3=8,则z^3+z^2+2z+2=___________
已知虚数z满足z^3=8,则z^3+z^2+2z+2=__________

已知虚数z满足z^3=8,则z^3+z^2+2z+2=___________已知虚数z满足z^3=8,则z^3+z^2+2z+2=__________
令w^3=1 即(w-1)(w^2+w+1)=0则w^2+w+1=0 w-1=0
z/2=w 则w=2z
原式化为8w^3+4w^2+4w+2=8w^3+4(w^2+w+1)-2=8+0-2=6
结果为6

z^2=-1,z=-8
所以z^3+z^2+2z+2=8+z^2+2z+2=8-1+2*(-8)+2=-7