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=__________
问题描述：
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=__________
答
z^2=-1,z=-8
所以z^3+z^2+2z+2=8+z^2+2z+2=8-1+2*(-8)+2=-7
答
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