I was confronted with this problem and wasn't able to find the supposed answer:
$$ {\partial_t |ψ|^2}={\partial_t (\bar{ψ}ψ)}={\partial_t\bar{ψ} *ψ+\bar{ψ}*\partial_t ψ}={-\frac{i\hbar}{2m}Δ\bar{ψ}ψ+\frac{i\hbar}{2m}\bar{ψ}Δψ}={-\frac{i\hbar}{2m}div(\nabla\bar{ψ}ψ-\bar{ψ}\nablaψ)=\frac{\hbar}{m}div(\Im(\bar{ψ}\nablaψ))}$$
I calculated it over and over, but eventually got the same sign error:
${-\frac{\hbar}{m}div(\Im(\bar{ψ}\nablaψ))}$ instead of ${\frac{\hbar}{m}div(\Im(\bar{ψ}\nablaψ))}$
I used the $\bar{z}-z=-2ib=-2i\Im(z)$ approach. In my understanding this should result in the cancellation of $-2$ and $-\frac{1}{2}$, leaving us with $\frac{i\hbar}{m}div(i\Im(\bar{ψ}\nablaψ))$. $i^2= -1$ => ${-\frac{\hbar}{m}div(\Im(\bar{ψ}\nablaψ))}$
I would appreciate an answer, because, at this point, I'm just desperate. Thank you in advance!