Z=（1+i）/2^0.5
则Z=2^0.5（cosπ/4+isinπ/4)/2^0.5=cosπ/4+isinπ/4
根据棣莫佛定理：
z^50=cos50π/4+isin50π/4=i
z^100=cos100π/4+isin100π/4=-1
则
1+Z^50+Z^100=1+i-1=i