I haven't worked out the whole thing but I think that the fact that the indices in the result are multiples of 4 would lead to looking at z= i. Recall that if z= i, then , , and [itex]z^4= 1[/tex]. That is, taking z= i gives, as real part, .
Thanx...
it actually worked..
I took z = i, then -i, then 1, then -1. the complex part vanishes and I got a system of two equations two unknowns : (z0 + z4 + z8 + ...) and (z2 + z6 + z10 + ... )