Starting at: $ a+\left(\left(\frac{i-a}{\gamma+1}\right)(\gamma+1)(i-a)^{\gamma}\right)^{\frac{1}{\gamma+1}} $
gives:
$ a+\left(\frac{(i-a)(\gamma+1)(i-a)^{\gamma}}{(\gamma+1)}\right)^{\frac{1}{\gamma+1}} $
which reduces to:
$ a+(i-a)^{\frac{\gamma+1}{\gamma+1}} $
and finally becomes:
$ i $
However, inserting values like: $a=1$, $i=-3$, and $\gamma=-3$ gives $5$ rather than $-3$ (for $i$) as the result. Interestingly with the "+'' between the terms changed to "-'', it works:
$a-\left(\frac{(i-a)(\gamma+1)(i-a)^{\gamma}}{(\gamma+1)}\right)^{\frac{1}{\gamma+1}}=-3$
I guess I did something in the above symbolic simplification that is not allowed (such that I miss a change in the "+" sign). However, I have no idea what! The parameters are in general constrained like this: $a=\{0,1\},$ $i<0$ (if $a=0$) and $i<1$ (if $a=1$), $\gamma<-1$.