In n  is a positive integer but not a multiple of 3 and z=−1+i3 , (where i=−1 ) then (z2n+2nzn+22n)  is equal to:

Since,       z=−1+i3            =2(−1+i32)           =2ω (cube root of unity)∴     z2n+2nzn+22n=22nω2n+2n.2nωn+22n                                =22n(ω2n+ωn+1)Let             n=3m+1,m∈I  or n=3m+2 , m∈I                      =22n(ω2+ω+1)=0