The distance from zero.
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No. Absolute value applies to the set of real numbers.
Two (assuming you are talking about real numbers). In general, for any given positive number, there will be two real numbers whose absolute value is that given number. In the case of complex numbers, the answer is "infinitely many" - all the numbers on a circle centered on the origin, with that radius, have that absolute value.
There are two real numbers and infinitely many complex numbers.
the range is all real numbers
In Real numbers, each is the additive inverse of the other.