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Additive Inverses is the proper term but the term zero pairs is also used.
will always be zero
Two integers which sum to zero (e.g. 3 and -3) are additive inverses of each other. All pairs of additive inverses sum to 0 and all pairs of integers which sum to 0 are additive inverses.
They will be the same absolute value with opposite signs. They don't even have to be integers.
Two integerss add to zero when their absolute values are equal and they have opposite signs.