虚数z满足z^3=8,z^3+z^2+2z+2=

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虚数z满足z^3=8,z^3+z^2+2z+2=
虚数z满足z^3=8,z^3+z^2+2z+2=

虚数z满足z^3=8,z^3+z^2+2z+2=
z^3=8
(z-2)(z^2+2z+4)=0 因为z是虚数所以
z^2+2z+4=0
z^3+z^2+2z+2=z^3+(z^2+2z+4)-2=z^3-2=8-2=6

Z^3-8=(z-2)(z^2+2z+4)=0
显然z不=2，所以z-2不=0
z^2+2z+4=0
z^2+2z+2=-2
这样就搞定了~~

设z=x+yi
z^3=(x+yi)^3=x^3+3x^2*yi-3xy^2-y^3*i=8
所以3x^2*y-y^3=0
因为y不等于0，所以y=正负根(3)x
因为x^3-3xy^2=8，将y=正负根(3)x代入得 x=-1
此时z=-1+根(3)i或-1-根(3)i
所以z^3+z^2+2z+2＝6

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