Hi,
let's try on this one;
Z^n = 1; many possibilities are ther.
As you know any number that is rised to 0 is equal to 1; You may also think of picking numbers to see that ; if n is odd (>0) then Z sould be 1, but if n is even (>0) then Z may be 1 or (-1); Therfore, this first stem can lead to many solutions;

1) tells that n is a non zero integer, that's fine because it eliminates the infinite possibilities of Z. , BUT this doesnt help to get a specific solution as just explained above

2) States for Z >0, we should pay attention that for Z to be equal to 1, n must be non zero inetger; which is just stated in the first option;

Thus, answer is C;

good luck

Thank you.


-ve integers sometime slip out of my mind. I've gotta keep track of them.

I understand the logic behind the answer, but I'm still a tad confused because I don't understand why z cannot be a non-integer, like the square root of 1.

IF
1) n is a nonzero integer
AND
2) z > 0
z could be the sqroot of 1

An example of this is when n = 2 (satisfying condition 1)
z = 1 (satisfying condition 2)

BUT when n = 1 (satisfying condition 1)
z = sqroot 1 (satisfying condition 1)

which would mean we could not solve for z based on this information.

Am I missing something obvious?

Thanks for your help!

Yes, I clearly was missing something. Thanks, Ian. I think I need a nap!