(4k+1)i^(4k)=(4k+1)
(4k+2)i^(4k+1)=(4k+2)i
(4k+3)i^(4k+2)=-(4k+3)
(4k+4)i^(4k+3)=-(4k+4)i
其中k=0,1,2.
1+2i+3i^2+……+2008i^2007=(1+5+...+2005)+(2+6+...+2006)i-(3+7+...+2007)-(4+8+...+2008)i
=502*(1+2005)/2+[502*(2+2006)/2]i-502*(3+2007)/2-[502*(4+2008)/2]i
=-1004-1004i