Very weird number?

Question

I did some weird fiddling with math and I got a number such that divided by itself = -1. It is somehow related to i (imaginary). Somebody tell me what's going on?

No zeros.
If such a number exists, then an axis could have THREE directions, instead of the usual 2. I wrote origional idea for it is in a one of my math books, but I can't find it.
I can't figure out what happens when it is added to another regular number though.

Ok, look at this:
let \(f(x)) = square root of x
let A be positive
let B be negative
let I be my number

\(A)= positive
\(B)= positive imaginary
\(I)= negative (I think,I really didn't work
on this)
A/A = 1
B/B = 1
I/I = -1
However, I did something such that there is a number with a magnitude and a sign, but neither positive nor negative, otherwise the number can't exist.

And so therefore, it doesn't apply to the old standard Cartesian coordeinate system, which has lines dominated by only two points, instead of my three.

Answer 1

Any number, other than zero, divided by itself is one. Zero divided by zero is undefined.

You didn't give much to go on. But if you were working with variables you may have divided by zero at some point without realizing it.

If you want more you need to be more specific.

Answer 2

Sorry to tell you this, but you have a logical mistake. All numbers, including complex and imaginary numbers, except zero, have the property that x / x = 1.

The most common mistake for this is to assume that the square root of a number has only one value. But in fact, square roots have TWO values. For example, sqrt(-1) = +i or -i. So the operation of taking the square root does not produce "a" number, it produces two numbers.