If z is a complex number satisfying
z + z^(−1) = 1, then z^n + z^(−n) , n ∈ N, has
the value
(1) 2(−1)^n , when n is a multiple of 3
(2) (−1)^(n−1) , when n is not a multiple of
3
(3) (−1)^(n+1) , when n is a multiple of 3
(4) 0 when n is not a multiple of 3
|