Reduce[(-1)^n + (-1)^(n + 1) == 0, n, Integers]
Reduce[(-1)^n + (-1)^(n + 1) == 0 &&
n \[Element] Integers, n, Complexes]
Reduce[(-1)^n + (-1)^(n + 1) == 0, n]
Reduce[(-1)^n + (-1)^(n + 1) == 0, n, Complexes]
Reduce[(-1)^n + (-1)^(n + 1) == 0, n, Reals]
(-1)^(-1/2) + -1^(1/2) == 0