Find the modulus of (1+i)^2008 + (1-i)^2008 = ?
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 and . Converting back to Cartesians enables you to add them and find the modulus.