BArg[k_]:=(π/6)k;
B[k_]:=Exp[BArg[k] I];
(* table the factor products *)
Table[{k,Simplify [(B[k]-B)(B[12-k]-B)]},{k,1,5}]
(* the functions z_t *)
Table[{k,Cos[BArg[k] t],Sin[BArg[k] t]},{k,1,5}]
(* the period of these function *)
Table[{k,((2 π)/(BArg[k]))},{k,1,5}]
(* the frequency of these functions in terms of cylces a year (one year has 12 units) *)
Table[{k,12/(((2 π)/(BArg[k])))},{k,1,5}]