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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
by Adrock 2y ago
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...
- deleted 2y ago[deleted]
- kgwgk 2y agoEven 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 2y agoyou are calculating inner product of otrhogonal vectors. For distance it should be abs(a-b) it will result to sqrt(2).
- deleted 2y ago[deleted]
- Adrock 2y agoSorry, it was a poor reference to this: https://www.reddit.com/r/mathmemes/s/c7gtvXrnz8 https://www.reddit.com/r/mathmemes/s/c7gtvXrnz8
- Someone 2y ago> 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...