>>10828076The basic geometry you learn in elementary school is all done without a reference system. This means that length can only be a positive real number, not because of some made-up crazy rule but just because it represents a physical observable that is described by a positive real number. If you could observe an imaginary length, than we would have to add that to the rules of the game and you could in fact have an object that occupies "negative area" or volume. This could actually be a useful representation for some physical phenomenon, which is why things like resistivity or the dielectric function can have imaginary parts. Not because there is actually something invisible or imaginary going on, just because the imaginary part describes some dynamic behavior that needs to be set apart from the ordinary real value. But as far as geometry goes, nobody normally needs to describe negative area, so we stick to positive real values.
Now in a reference system this changes a little. In a reference system you have a number of lines (3 for 3D space) that intersect at an origin. In one direction of each line are positive numbers, in the other negative numbers. So if you look at this you might be tempted to, for example, choose the point -3 on the x axis, the point 2 on the y axis and think that you have now a rectangle of area (-3)*2= -6. And yet if you draw this on a squared sheet of paper you can count the number of squares in this rectangle and find to obviously be 6, not -6. This means that, while the point you chose was -3, the length of that side of the rectangle is still 3, not minus -3 as the point would seem to indicate. This is a naive approach to the concept of modulus. Imagine an arrow that, starting from the origin of the RS, points right to the point -3 on the x axis. This is called a vector. The vector is completely described by the point -3, but its length, or modulus, is actually 3.
Now picture a RS with two axis. You should be used to see x and y.
