已知z=-(1+i)/√2,则z^100+z^50+1=

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答案和解析

z=-(1+i)/√2
z^2=(1-1+2i)/2=i
z^4=-1
z^100=z^4^25=-1
z^50=z^2^25=i^25=i
故z^100+z^50+1=i

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