n must be even, or else the two bases in the exponent would be equal, which is impossible.
if n is even, either z or z+1/z is negative. if z is negative, then -z=z+1/z or 2z=-1/z, and 2z^2=-1 which is imposssible.
then z+1/z is negative. then -z-1/z=z, so 2z=-1/z and 2z^2=-1 which is also impossible.
so from what i get, there are no possible solutions for n such that there is a solution for z.
HOPE THIS HELPED!!
