Đáp án đúng: C Ta có $S=C_{{2010}}^{0}+{{i}^{2}}C_{{2010}}^{2}+{{i}^{4}}C_{{2010}}^{4}+...+{{i}^{{2010}}}C_{{2010}}^{{2010}}=>S=\frac{{{{{\left( {1+i} \right)}}^{{2010}}}+{{{\left( {1-i} \right)}}^{{2010}}}}}{2}.$ Mà có${{\left( {1+i} \right)}^{{2010}}}={{\left( {\sqrt{2}} \right)}^{{2010}}}.cos\frac{{2010\pi }}{4}.$ Suy ra S = 0.