• ## Discover

1. Home >
2. All Categories >
3. Science & Mathematics >
4. Mathematics >
5. Resolved Question
Member since:
March 01, 2012
Total points:
187 (Level 1)

## Resolved Question

Show me another »

# Can someone please explain this to me?

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!!!
Member since:
October 19, 2011
Total points:
2,590 (Level 4)

## Best Answer - Chosen by Voters

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)
100% 1 Vote

There are currently no comments for this question.

This question about "Can someone please e… " was originally asked on Yahoo Answers United States

### Other Answers (2)

• Member since:
October 04, 2011
Total points:
742 (Level 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
• Member since:
June 06, 2008
Total points:
267 (Level 2)
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

## Discover Questions in Mathematics

Yahoo does not evaluate or guarantee the accuracy of any Yahoo Answers content. Click here for the Full Disclaimer.

Help us improve Yahoo Answers. Tell us what you think.