Square Root of Negative One

[segadragon]

What is it?

What times itself is -1? Is negative one squared equal to negative one? It makes sense, since 1²=1.

However, try it in your calculator. (-1)²=1.
(A negative times a negative is a positive)

If you're getting -1, it's because your calculator is taking the opposite of one squared. Make sure you use the parenthesis feature of your calculator (if it has one) and wrap -1 in parenthesis, leaving the ² outside of it.

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Remember what I said earlier. "A negative times a negative is a positive."
This means that no negative number squared is -1.
We all should also know that any positive number squared is a positive. Which means no positive number squared is -1.

The square root of negative one is an "imaginary number." It's referred to as i. There is no definite answer. Sorry.

[realillusion]

Actually, there is a definitive answer, and you gave it. The square root of negative one is i. Just like "theoretical entities" in science, i is something that "everyone" believes in because even if we can't represent the value physically it is still scientific in that it consistently explains other phenomena. There is a lot of math behind i, not the least of which is Euler's Identity, which basically single handedly makes Ordinary Differential Equations possible for any order 2 or greater... I only use this example because it's the one youre most likely to encounter in highschool.

So, basically, there is definitely an answer, and if your calculator-happy self wants to check that, put i^2 in your calculator: VIOLA! -1.

[Wrinkley Ninja]

There is an answer i learnt this ages back (a year or 2), and the answer is not i (known as little i)

The correct answer to this is:

E i ]-[ + -1 = -1

Hm, its the closest i could get it to with a keyboard, might have to draw it our on photoshop to show you the correct answer, but i'll tell you what each means.

E = Energy
i = little i
]-[ = Pie
+
-1

IT should be right, man totally forgot about this, haha. I was told this is a University question, so learn it quick.

[segadragon]

I don't know what "Energy" has to do with math. You'd use that in Science. And you can't say "little i" isn't the square root of negative one, then use "little i" to solve for it.

Define "Energy" and "little i."

Also, what yours says is E*i = 0.
Your problem doesn't find the square root anywhere. What I think this is is a problem in which you use "little i," not solve for it.

]-[ = Pie

It's Pi.

[Who?]

Mmm, yeah, I just went over this this year, the square root of negative one is "imaginary". The root is represented as (as realillusion stated) "i". Supposedly, it's often used in physics. Because it's imaginary, it's a construct that can't really be found using known math methods. It's like... erm... those postulates... or whatever... that you have to assume in Euclidean (sp?) math.