I recently was working with square roots and came across this-
$({\sqrt -1})$$=-1^\frac12$$=-1^\frac24$$=(-1^2)^\frac14$$=1^\frac14$$=1$
I understand that this is not true,but despite repeated attempts failed to prove it wrong.Can someone please point out the fallacy in this proof.Thanks in advance.
The fourth root of $1$ has four solutions: $1$, $-1$, $j$ and $-j$. The last two solutions are identical to the two solutions of the square root of $-1$.