∵z=1+ 2i 1?i =1+ 2i(1+i) 2 =i，∵i2=-1，i4=1，∴1+z+z2+…+z2010为=1+i+i2+…+i2010= 1?i2011 1?i = 1?i3 1?i ＝ (1?i)?(1+i+i2) 1?i ＝i；故选C．
