it can be having 3 values
if n is not equal to zero, then z^n = z^0 or n=0
or z can be equal to 1 or -1
now statement 1) says n is non zero, it is insufficient because z can be 1 or -1
statement 2 ) says z>0 it also leaves with 2 value of z, 1 or any thing if n is not equal to 0.
but if we combine both the statement we get z = 1
so answer is C