Absolute value is best thought about geometrically. It is the length of a line segment between two points regardless of what quadrant that line segment happens to be in. Thus a line segment stretching from 0 to -3 is, obviously, 3 units long. So is a line segment stretching from 0 to 3. Or 0 to 3i in complex space. If you fail to think about it geometrically, it seems a little abstract or even weird, so that’s why the geometrical intuition is best. Technically we say:
Dot (inner, scalar) product
See entry on dot product for more.