Can someone please explain this to me?

Question

Ok so i'm 13 and recently learned about imaginary numbers, that i is the square root of -1. I was thinking about this last night and i formulated a proof to say that the square root of -1 is not imaginary and in fact -1.

Here is the proof:
i = SR (square root) of -1
i^2 = -1 (i squared both sides)
-i^2 = 1 (i multiplyed both sides by -1)
-i = 1 (i square rooted both sides)
i = -1 (I multiplyed both sides by -1)

So therefore, the square root of -1 is -1 itself.

P.S: Please don't hesitiate on telling me i'm wrong as i love to learn and i would like to find out why scientists think that i is an imaginary number, if this is true. Thanks for answering!!!

Answer 1

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I thought that at first two! The reason i is imaginary is because you can't find the square root of a negative. 1 times 1= 1 and -1 times -1 also equals one because a negative times a negative equals a positive so therefore no number can really = the square root of - 1.

These are correct:
i = SR (square root) of -1
i^2 = -1 (i squared both sides)
-i^2 = 1 (i multiplyed both sides by -1)

These two are incorrect:
-i = 1 (i square rooted both sides)
i = -1 (I multiplyed both sides by -1)

Answer 2

Well first and foremost you cannot take a sqrt of a negative number according to modern mathematics, but what you're saying is that you are...

√-1=i
-1=i²
1=-i²
0=-1-i²
0=0

√-1=i
(√-1)²=(i)²
1=1

Unfortunately this is all assuming that √-1=i

The main question here should be which came first, Roots or Powers?

Because -1²=1
and √(-1²)=√(1)
-1=1 Not true...Even though in theory it would work depending on how you think of it...but eh...The world of mathematics is weird for example: 0/0

Is it 0, 1, Infinity?

But, eh...Whatever.

Why don't you study imaginary numbers and prove to everyone someday that this is so, that in fact √-1=-1

(And unfortunately you can't just do -1√-1=√1=1*-1=-1)

Good luck with your theory.

Source(s):

AP Calculus

Answer 3

You are very smart! Just one little mistake..

on your third step: -i^2 = 1
to your fourth step, there is an error.
Your proof would only work if it was (-i)^2. But no. It is -i^2 meaning the i is the only thing being squared. You look at it like you are taking the square root of a square, but that only works if the square is by itself. It isn't, there is a -1 times to it. That mistake makes the rest of the proof invalid