虚数z满足z^3+z=0 则1+z+z^2+…+z^100=
问题描述：
虚数z满足z^3+z=0 则1+z+z^2+…+z^100=
答
z（z^2+1）=0因为z是虚数,所以z≠0,于是z^2+1=0所以,z=±i于是,1+z+z^2+z^3=0所以,1+z+z^2+…+z^100=（1+z+z^2+z^3）+（z^4+z^5+z^6+z^7）+……+（z^96+z^97+z^98+z^99）+z^100=0+0+……+0+z^100=1...