2. Simplify $(\mathrm{i}+1)^{2016}+(\mathrm{i}-1)^{2016}=$
2. $2^{1009}$.

From $(i+1)^{2}=2 i \Rightarrow(i+1)^{2016}=2^{1008}$.
Similarly, $(i-1)^{2016}=2^{1008}$.
Therefore, $(i+1)^{2016}+(i-1)^{2016}=2^{1009}$.