∵ z^2+z+1=0,
∴ (z-1)(z^2+z+1)=0,即
z^3-1=0,
z^3=1.
z^100+z^50
=z*z^99+z^2*z^48
=z*(z^3)^33+z^2*(z^3)^16
=z+z^2
=-1
即 z^100+z^50=-1.
∵ z^2+z+1=0,
∴ (z-1)(z^2+z+1)=0,即
z^3-1=0,
z^3=1.
z^100+z^50
=z*z^99+z^2*z^48
=z*(z^3)^33+z^2*(z^3)^16
=z+z^2
=-1
即 z^100+z^50=-1.