I Another negative one equals one proof

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1. Mar 30, 2017

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.

2. Mar 30, 2017

Staff: Mentor

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

3. Mar 30, 2017

Staff: Mentor

4. Mar 30, 2017

Vanadium 50

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

5. Mar 30, 2017

Ajgrinds

Yeah, thanks

6. Mar 30, 2017

Ajgrinds

4rt them both...

7. Mar 30, 2017

Staff: Mentor

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

8. Mar 30, 2017

Staff: Mentor

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

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

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