I was talking to a friend about the problem with this proof and I'm stomped on the illegal step:
$i = (-1)^{(1/2)}= (-1)^{(2/4)} =((-1)^2)^{(1/4)} = 1^{(1/4)} = 1$
I was talking to a friend about the problem with this proof and I'm stomped on the illegal step:
$i = (-1)^{(1/2)}= (-1)^{(2/4)} =((-1)^2)^{(1/4)} = 1^{(1/4)} = 1$
This is wrong for the same reason that the following proof is wrong: $$-1 = (-1)^{(2/2)} = (-1^2)^{(1/2)} = 1^{(1/2)} = 1$$ 1 is $a$ 'square root of unity', but it's not unique.