Problem with definition

Problem with definition

Posers and Puzzles

Cookies help us deliver our Services. By using our Services or clicking I agree, you agree to our use of cookies. Learn More.

e

Joined
31 Jan 04
Moves
331
07 Mar 04

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.

F
Artist in Drawing

in your fridge

Joined
21 May 03
Moves
9766
07 Mar 04

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.

e

Joined
31 Jan 04
Moves
331
08 Mar 04

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.