Something something distance calls for norm, not just squares.

||i||² + ||1||² = 2

no, d..do you have a plan?

Imagining your death. :P

But seriously, it's perfectly sensible when remember that i is just the mathematical representation of "left turn", just like -1 is the mathematical representation of "go backwards"-- and as we know, two left turns sends you backwards. So think about this triangle in the following way:

Imagine you are a snail, starting at the origin. Now imagine that you walk forward 1 step along the horizontal line. Then you turn 90° to the left to start walking along the vertical line, but then, because you need to walk i steps along this line you take another 90° turn to the left, which means that you are now walking backwards and you end up back at the origin. How far away from the origin are you? Zero steps.

This one made me laugh almost as much as the OP. Thank you!