The last digit of (1001)²⁰⁰⁸ + (1002) = ?

$$\eqalign{ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{(1001)^{2008}} + (1002) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, \downarrow \cr & {\text{unit digit}} \to {\text{ }}{{\text{1}}^{2008}} + 1002 \cr} $$
Unit digit will be 1 in case of 1 respective of power
⇒ 1 + 1002 = 1003
⇒ 3 unit digit (last digit)