# Why we say $i^2 = -1$ while it is $1$

If we have $$\sqrt[2]{x}^{2} = \sqrt[2]{x^2} = |x|$$ so : $$\sqrt[2]{-1}^{2} = \sqrt[2]{-1^2} = |-1| = 1$$ so why we say $i^2 = -1$?

• Well I say that $i^2$ equals $-1$ because it equals $-1$. I don't say $i^2$ equal $1$ because it doesn't equal $1$. Nov 29, 2017 at 19:28
• This question is massively a duplicate, but I can't find the One True Answer - math.stackexchange.com/questions/1096917/… is an example. Nov 29, 2017 at 19:30
• Logical reason? It's the definition of $i$... Nov 29, 2017 at 19:31

$$\sqrt{x^2}\neq (\sqrt{x})^2$$