If z^n = 1, what is the value of z?

[BTGModeratorVI]

If z^n = 1, what is the value of z?

(1) n is a non zero integer
(2) z > 0

Answer: C
Source: official guide

[Brent@GMATPrepNow]

If z^n = 1, what is the value of z?

(1) n is a non zero integer
(2) z > 0

Answer: C
Source: official guide

Target question: What is the value of z?

Given: [m]z^n = 1[/m]
There are 3 possible cases in which the above equation holds true. When a given piece of information yields a small handful of possible cases, I often find it useful to list the possible cases before dealing with the statements (which I've already scanned)
case i: z is any integer, and n = 0 (e.g., [m]5^0 = 1[/m])
case ii: z = 1, and n is any number (e.g., [m]1^3 = 1[/m])
case iii: z = -1, and n is any EVEN INTEGER (e.g., [m](-1)^4 = 1[/m])

Statement 1: n is a non zero integer
This means we're dealing with EITHER case ii OR case iii. Since cases ii and iii yield different answers to the target question, statement 1 is NOT SUFFICIENT

Statement 2: z > 0
This means we're dealing with EITHER case i OR case ii. Since cases i and ii yield different answers to the target question, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us we're dealing with case ii or case iii
Statement 2 tells us we're dealing with case i or case ii
Since only case ii satisfies both statements, it must be the case that z = 1, and n is any number
Since we can be certain that z = 1, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent