I Another negative one equals one proof

[Ajgrinds]

Hey guys! I need help proving why this proof is wrong. I know it's wrong, but I can't figure out why. Anyway:
i = sqrt -1
i^4 = 1
1^4 = 1
Substution: i^4 =1^4
i = 1
1 = sqrt -1
1^2 = -1
1 = 1^2
1= -1

If you have any questions, feel free to ask.

 

[mfb]

Substution: i^4 =1^4
i = 1

That step is not valid. Just dropping exponents doesn't even work for real numbers.

 

[fresh_42]

https://www.physicsforums.com/insights/things-can-go-wrong-complex-numbers/

 

[Vanadium 50]

-1^2 = 1^2 therefore -1 = 1. Same idea. Do you see where this fails? No need to drag i into it.

 

[Ajgrinds]

-1^2 = 1^2 therefore -1 = 1. Same idea. Do you see where this fails? No need to drag i into it.

Yeah, thanks

 

[Ajgrinds]

That step is not valid. Just dropping exponents doesn't even work for real numbers.

4rt them both...

 

[mfb]

4rt them both...

$(-1)^4 = 1^4$, but obviously $-1 \neq 1$.
This is the one-step version of post 1.

 

[Mark44]

-1^2 = 1^2 therefore -1 = 1.

But -1^2 ≠ 1^2, as I'm sure you know...

However, (-1)^2 does equal 1^2.