Question

Can two different numbers have the same absolute value?

Answer 1

Yes.

Explanation:

Absolute value is the magnitude of a number irrespective of its sign.

Hence there can be two real numbers with different signs such `+a` and `-a` who have an absolute value of `a`. Other examples could be `+1.01001000100001.....` and `-1.01001000100001.....` who have different signs but same absolute value, or for that matter `-root(3)73` and `+root(3)73`.

Hence if domain is real number for each absolute value there are two different numbers one can have with same absolute value.

However, if domain is Complex numbers, absolute value of a number `a+bi` is `sqrt(a^2+b^2)` and for each absolute value there could be infinite different numbers with same absolute value.

For example, `3+4i`, `-4+3i`, `1+i2sqrt6`, `-5-i2sqrt5`, `-5i` all have an absolute value of `5`.