Problem with definition

Originally posted by TheMaster37
Ok, i'm going to pay attention to teachers in the future. They should introduce i with the remark that i is A number with the property i^2 = -1, not THE number.

There is something I think that I need to clarify for you, which it seems you may have a misunderstanding of: there is a difference between the inverse 'function' of the squared function (being the squrt 'function'😉, and the algibraic inverse of the squared function (being +-squrt).
If you have x^2=4, then to find out what x is then you would take the inverse the the square (being '+-sqrt'😉 such that +-sqrt(x^2)=+-sqrt(4), which becomes: x=+-2. This is true because both positive and negative 2 squared equal 4.
You must understand that +-sqrt is the true inverse of x^2, but +-sqrt is not a function. Yet, when you reference the idea of 'sqrt', you are referencing the function of 'sqrt', which only recognizes the positive values of x.

sqrt(-1), is the sqrt 'function' of -1, which is only positive i.

I hope that is more clear.

Originally posted by TheMaster37
Ok, i'm going to pay attention to teachers in the future. They should introduce i with the remark that i is A number with the property i^2 = -1, not THE number.

for your information, the teacher did. Check your book about complex functions, it is all there in paragraph 2.

Originally posted by econundrum
[b]There is something I think that I need to clarify for you, which it seems you may have a misunderstanding of...

I'm sorry, but I think I should take that statement back. When I read your post which prompted me to write that, I misread it. Everything else I stated in my last post was accruate, but not necessarily that you had a misunderstanding of the sqrt function.
My mistake was seeing your post which showed i^2=-1 and not noticing the i (I had assumed you had put x^2=-1). Sorry for the mix-up.