Originally Posted by
Prove It My objection is that your answer is not fully simplified. To get full marks I'm sure that the OP would need to get a single number as their answer, not a sum (after all, a modulus represents the LENGTH of a complex number). And I know that you are not going to physically sum 1005 terms...
Meanwhile, using DeMoivre's Theorem, as Mr F suggested, enables you to quickly evaluate $\displaystyle \displaystyle (1 + i)^{2008}$ and $\displaystyle \displaystyle (1 - i)^{2008}$. Converting back to Cartesians enables you to add them and find the modulus.