I was looking on this post http://www.songho.ca/math/euler/euler.html and I came to the comment that says "i is not a number at all. It is an ill-formed concept. There is a vast difference between a magnitude and a number. The objects you think of as" complex numbers" are not numbers of any kind whatsoever. They are quasi-mathematical objects."
by wiki a mathematical object is "In mathematical practice, an object is anything that has been (or could be) formally defined, and with which one may do deductive reasoning and mathematical proofs."
I tried to search over internet about the term "quasi mathematical object" but it just says about literal meaning. I wonder what are they? or there is no such term exist in mathematics?
EDIT: I am not agree with the comment (that i is not a number) but I am stuck with the term "Quasi mathematical object" so I even understand the meaning of it but is there such a thing exist? I am more looking for example if the term "quasi mathematical object" exist. If not then I should delete this post. Thanks for taking your time.
That comment looks to be from someone who has not studied mathematics rigorously and could well be a physicist or engineer etc who uses number systems but doesn't study them specifically (controversial comment but hear me out).
When he says i is not a number he is quite correct if he restricts himself to the 'usual' number systems of $\mathbb{N},~ \mathbb{Z},~ \mathbb{Q}$ and $\mathbb{R}$. And it appears that this is exactly what he is doing. However, a number system is more generally a set with operations between the elements which form a group, a ring or some other algebraic object. It is precisely as one of these algebraic objects that we define the complex numbers, they exist abstractly without needing any geometric interpretation. This is I think where the writer of that comment has misunderstood. Complex numbers aren't some convenient addition to the reals that we glued on to make pretty shapes, it is a fundamental extension of the real numbers that exists very naturally and we need in order for instance to have well defined roots of polynomial equations.
In conclusion I don't think that the writer of that comment knows what they are talking about, complex numbers are fundamental, hugely important, natural and elegant and are in no way ill-formed whatsoever.
Reply to question edit:
I have never ever heard the term 'quasi-mathematical object', I believe that it was made up by the person posting the comment.