Dear Sathyaram
a (alpha) b (beta) a+b =1 so (a+b)^2012=1 now (a-b)^2=(a+b)^2-2ab=1-2=-1 so a-b whole square =-1 hence a-b=i (iota),(a-b)^2012=i^2012=1 so answer is 1+1=2 , Please Approve my answer if you have understood the solution
Regards
Noaman Ali