z^n = 1

[joannabanana]

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

1. n is a non zero integer.

2. z > 0.

The official answer is C - both statements are needed.

My question is why isn't stmt 2 sufficient? What else could z be other than 1?

[Rahul@gurome]

If z^n = 1, what is the value of z?
1. n is a non zero integer.
2. z > 0.

The official answer is C - both statements are needed.
My question is why isn't stmt 2 sufficient? What else could z be other than 1?

It's not only the value of z that makes z^n equals to 1! Value of n also has a part in it. For n = 0, z could be any number, even fractions. Thus z > 0 is not sufficient.

Given: z^n = 1

Statement 1: n is a non zero integer.
1 raise to any power is equal to 1 and -1 raise to any even power is also equal to 1. Thus z can be 1 for any value of n or z can be -1 for even values of n.

Not sufficient.

Statement 2: z > 0
No restrictions on n. For n = 0, z could be any number, even fractions.

Not sufficient.

1 & 2 Together: Only possible value of z is 1.

Sufficient.

The correct answer is C.

[joannabanana]

Yes, of course! Anything to the power 0 = 1 Silly me!

Now the goal is to not forget these kinds of things in the actual exam!