2. Let $\mathrm{i}$ be the imaginary unit, simplify $(\mathrm{i}+1)^{2016}+(\mathrm{i}-1)^{2016}=$
$$
(i+1)^{2016}+(i-1)^{2016}=(2 \mathrm{i})^{1008}+(-2 \mathrm{i})^{1008}=2^{1009}
$$

Translate the above text into English, please keep the original text's line breaks and format, and output the translation result directly.

$$
(i+1)^{2016}+(i-1)^{2016}=(2 \mathrm{i})^{1008}+(-2 \mathrm{i})^{1008}=2^{1009}
$$