Got it. The similarity between this and the other question I just asked was throwing me off. Thanks.
The way you solved them.
Or, is it because a and b could take on a positive and negative value? For example, a=10 and b=-10 whereas |a| and |b| but be positive so the only way they can = zero is if a and b are both zero?
|m| and |n| are non-negative, not positive. The sum of two non-negative values can be zero only if both are 0. Thus m=n=0.
As for m = -n. Infinitely many case are possible, m=n=0, m=-n=1, m=-n=2, ...