$S$ is domain(open set and connected) and $\gamma$ is closed curve in $S$ . If $f(z)$ analytic on $S$ and $f'(z)$ continous on $S$

Question

$S$ is domain(open set and connected) and $\gamma$ is closed curve in $S$ . If $f(z)$ analytic on $S$ and $f'(z)$ continous on $S$ . Show that $\int _\gamma \overline{f(z)}f'(z) dz$ is only imajiner part

I stuck to prove that the real part is zero -__-