I'm trying to show that any complete $\Sigma_1^0$ set is creative.
The definition of creative I understand is: if there is a total recurvise function f s.t. f(e) is an element of A iff f(e) is an element of W$_e$ for all e.
So can we construct a total recursive function for the set above? $\Sigma_1^0$ quantified is a bunch of OR conjunctions
$K=\{x:x\in W_{x}\}$, if $A$ is a complete r.e. set then there is a bijective recursive function s.t. $h:K\equiv A$, notice that $h^{-1}$ is also recursive, we denote $h^{-1}(W_{e})=W_{g(e)}$, so $h(W_{g(e)})=W_{e}$.
We claim that the $f=h\centerdot g$ meet the requirement:
$h(g(e))\in A\Leftrightarrow g(e)\in K\Leftrightarrow g(e)\in W_{g(e)}\Leftrightarrow h(g(e))\in W_{e}$