作业帮若虚数z满足z^3=8,则z^3+z^2+2z+2=多少?请帮我写下具体过程,
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若虚数z满足z^3=8,则z^3+z^2+2z+2=多少?请帮我写下具体过程,
若虚数z满足z^3=8,则z^3+z^2+2z+2=多少?
请帮我写下具体过程,
若虚数z满足z^3=8,则z^3+z^2+2z+2=多少?请帮我写下具体过程,
z^2-2^3=0
(z-2)(z^2+2z+2^2)=0
z为虚数,所以z-2≠0
z^2+2z+4=0
z^3+z^2+2z+2=z(z^2+2z+4)-(z^2+2z+4)+6=6
z^2-2^3=0
(z-2)(z^2+2z+2^2)=0
z^2+2z+4=0
z^3+z^2+2z+2=z(z^2+2z+4)-(z^2+2z+4)+6=6
z^2-2^3=0
(z-2)(z^2+2z+2^2)=0
z≠2
z^2+2z+4=0
z^3+z^2+2z+2
=z^3-2+(z^2+2z+4)=8-2=6
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