currently doing a bit of research on those, i have not been to a math class in a few years...Why do i get the feeling someone is going to end up posting their homework on this thread...looking at:
Whats wrong:

i = (-1)^{1/2} = ((-1)^{3})^{1/2} = (-1)^{3/2} = ((-1)^{1/2})^{3} = (i)^{3} = -i
\Rightarrow 1 = -1

Whats wrong:

x^2 - x^2 = x^2 - x^2
x(x - x) = (x - x)(x + x)
x = (x + x)
x = 2x
\Rightarrow 1 = 2