[Adrock]

A simple demonstration of why this is necessary is to consider the distance between the points 1 and i on the complex plane. If you naively compute the distance between them using the familiar Euclidean formula √(a²+b²) you get:

√(1²+i²) = √(1-1) = 0

That can't be right...

[Adrock]

Sorry, it was a poor reference to this:

https://www.reddit.com/r/mathmemes/s/c7gtvXrnz8

[Someone]

> If you naively compute the distance between them using the familiar Euclidean formula √(a²+b²)

That formula may be familiar, but it doesn’t compute a distance.

A simple demonstration of why this is necessary is to consider the distance between the points 3 and 4. If you naively compute the distance between them using the familiar Euclidean formula √(a²+b²) you get:

√(3²+4²) = √(9+16) = √(25) = 5

That can't be right...

[kgwgk]

Even simpler is trying to calculate |i| (i.e. the distance between the points 0 and i on the complex plane) as √i² = √-1 = i.

[nokan]

you are calculating inner product of otrhogonal vectors. For distance it should be abs(a-b) it will result to sqrt(2).