Proof that $i=1=-1$( Mathematical Fallacy)

Question

I thought of a proof that:-

$$i=-1=1$$

Here is the proof :-

$$ (i)^4=(i^2)^2 \\ = (\sqrt{-1})^4=(\sqrt{-1}^2)^2 \\ = (\sqrt{-1})^4=(-1)^2 \\ = (\sqrt{-1})^4=1 \\ \implies i^4=1 \\ \text{also} \\ -1^4=1 \\ \text{and} \\ 1^4=1 \\ \implies i^4=-1^4=1^4 \\ \implies i=-1=1$$ This is my proof but I know that there is some problem with last statement as it makes are number line collapse but don't you think that this is still a valid logical argument, if not why?

Is it possible that it is because of 1 is a unique number ( another reason to call it it unique).

Answer 1

If $a^4=b^4=c^4$, does that always mean $a=b=c$?