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Re: Z^n = 1, What is the value of Z? 1. n is a nonzero integer [#permalink]
13 Sep 2013, 06:32

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Re: If z^n = 1, what is the value of z? [#permalink]
13 Sep 2013, 07:56

Expert's post

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

(1) n is a non zero integer --> \(1^{any \ integer}=1\) and also \((-1)^{even}=1\), so \(z\) can be 1 or -1. Not sufficient.

(2) z > 0 --> any nonzero number to the power of 0 is 1, so if \(n=0\) then \(z\) can be any non-zero number (any positive number in our case as given that \(z>0\)). Not sufficient.

(1)+(2) \(n\) is a nonzero integer and \(z>0\) implies that \(z\) can equal to 1 only. Sufficient.

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