Z=（1-i）/√2 ,则Z^100+Z^50+1的值是?
问题描述：
Z=（1-i）/√2 ,则Z^100+Z^50+1的值是?
答
z=cos(-π/4)+isin(-π/4)所以原式=[cos(-100*π/4)+isin(-100*π/4)]+[cos(-50*π/4)+isin(-50*π/4)]+1=cos(-25π)+isin(-25π)+cos(-25/2π)+isin(-25/2π)+1=cosπ+isinπ+cos(-π/2)+isin(-π/2)+1=-1-i+1=-i...