You can’t have a distance in a “different direction”. That’s what the |x| is for, which is the modulus. If you rotate a triangle, the length of the sides don’t change.
The vector from one point to another in space has both a distance (magnitude) and a direction. Labeling the side with i only really makes sense if you say we’re looking at a vector of “i units that way”, and not at an assertion that these two points are a directionless i units apart. Then you’d have to break out the complex norms somebody mentioned.
You can’t have a distance in a “different direction”. That’s what the |x| is for, which is the modulus. If you rotate a triangle, the length of the sides don’t change.
The vector from one point to another in space has both a distance (magnitude) and a direction. Labeling the side with i only really makes sense if you say we’re looking at a vector of “i units that way”, and not at an assertion that these two points are a directionless i units apart. Then you’d have to break out the complex norms somebody mentioned.