[enriquto]

> What does it mean to multiply two points in the plane? You still need an additional rule for that.

yes, you do. I was answering the question of what complex numbers are. There are many things that you can do with them, that you need to define separately.

[darkscape]

Hmm, I tend to think that what one can do with some objects is an essential part of what they are.

Two-dimensional vectors can just as well be thought of as points in the plane. What sets complex numbers apart is eg that we define complex multiplication of them.

A more general example: a group is not just some set G, but that set with a binary operation satisfying certain axioms.

[ttoinou]

a 2D point is not enough to define complex numbers

[enriquto]

> a 2D point is not enough to define complex numbers

alright. Yet, one 2d point is certainly enough to define one complex number, which is what I meant.

The data is the same, but they have different methods.

[navane]

I struggle with this a lot, too. Maybe "complex numbers" is a misnomer, and we should call them "complex operations", or "complex methods".

I have a hunch that for math people complex numbers are tied really close to the operations you perform with them. But to me, the lay man, the numbers are just data.

From reading around on HN I infer that there are certain things that are grouped together because they share certain actions. Groups, sets, monads.

However, if you were to encounter the number (1, 5) in the wild, you wouldnt know if it was a complex number or just a 2 dimensional vector until it is operated upon.

[ttoinou]

The OP was looking for "explanation of complex numbers"

You won't explain anything by talking about 2D points only

But you can if you specify only how they behave with addition and multiplication (see my others posts)

[enriquto]

> The OP was looking for "explanation of complex numbers" > You won't explain anything by talking about 2D points only

The OP was complaining about the explanation that complex numbers "have a real and an imaginary part", because it mean nothing to them. It is alright, then, to clarify that this just means that they are points in the plane, and some operations will be defined on these points.

[ttoinou]

Yes