information:extraction
Powers of negative one

If n is an even integer, then (−1) = 1. This is because a negative number multiplied by another negative number cancels the sign, and thus gives a positive number.

If n is an odd integer, then (−1) = −1. This is because there will be a remaining −1 after removing −1 pairs.

Because of this, powers of −1 are useful for expressing alternating sequences. For a similar discussion of powers of the complex number i, see § nth roots of a complex number.