Absolute value of difference of squares contradiction

Question

Consider this formula:

$$\sqrt[4]{(z^2-1)^4}$$

If we expand it, we get $|z^2-1|$. Now, if $z=-1$, $|(-1)^2-1| = |1-1| = |0|$, so $|z^2-1| = z^2-1$.

On the other hand, $|z^2-1| = |z-1|*|z+1| = |-1-1|*|-1+1| = |-2|*|0|$, so $-(z-1)*(z+1) = -(z^2-1)$.

How's this possible?

Answer 1

This is not a contradiction. It just so happens that $$0=-0$$