I Another negative one equals one proof

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    Negative Proof
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The discussion centers on a flawed proof that attempts to equate the imaginary unit i with the number 1, ultimately leading to the incorrect conclusion that 1 equals -1. Key points highlight that the substitution of i^4 = 1^4 is invalid, as it improperly drops exponents without justification. Participants emphasize that while -1 squared equals 1 squared, this does not imply -1 equals 1. The consensus is that the proof fails due to incorrect manipulation of complex numbers and exponents. The conversation reinforces the importance of maintaining mathematical rigor when dealing with complex numbers.
Ajgrinds
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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.
 
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Ajgrinds said:
Substution: i^4 =1^4
i = 1
That step is not valid. Just dropping exponents doesn't even work for real numbers.
 
-1^2 = 1^2 therefore -1 = 1. Same idea. Do you see where this fails? No need to drag i into it.
 
Vanadium 50 said:
-1^2 = 1^2 therefore -1 = 1. Same idea. Do you see where this fails? No need to drag i into it.
Yeah, thanks
 
mfb said:
That step is not valid. Just dropping exponents doesn't even work for real numbers.
4rt them both...
 
Ajgrinds said:
4rt them both...
##(-1)^4 = 1^4##, but obviously ##-1 \neq 1##.
This is the one-step version of post 1.
 
Vanadium 50 said:
-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.
 

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