That’s not relevant to what they said, which is that distances can’t be imaginary. They’re correct. A metric takes nonnegative real values by definition
Why can’t a complex number be described in a Banach-Tarsky space?
In such a case the difference between any two complex numbers would be a distance. And sure, formally a distance would need be a scalar, but for most practical use anyone would understand a vector as a distance with a direction.
That’s not relevant to what they said, which is that distances can’t be imaginary. They’re correct. A metric takes nonnegative real values by definition
Why can’t a complex number be described in a Banach-Tarsky space?
In such a case the difference between any two complex numbers would be a distance. And sure, formally a distance would need be a scalar, but for most practical use anyone would understand a vector as a distance with a direction.
The distance between two complex numbers is the modulus or their difference, a real number