i,i^2,i^3,i^4是以4为周期进行变化的2011=4*502+3
1+2i+3i^2+...+2011i^2010
=(1+2i-3-4i)+(5+6i-7-8i)+...(2005+2006i-2007-2008i)+2009+2010i-2011
=(1+5+9+...2009)+i(2+6+10+...2010)-(3+7+11+...+2011)-(4+8+12+...+2008)i
=(1+2009)*503/2 +i(2+2010)*503/2 -(3+2011)*503/2 -i(4+2008)*502/2
=1005*503+1006*503i-1007*503-1006*502i
=-1006+1006i