I am trying to understand why:
$\left|\displaystyle{\int}_{\gamma}f\left(z\right)dz\right|=\displaystyle{\int}_{\gamma}\left|f\left(z\right)\right||dz|\iff\forall z$ on $\gamma$ it is $\text{arg}\left(f\left(z\right)\right)=\text{const.}$
where $\int_\gamma f(z)|dz|:=\int_a^bf(\gamma(t))|\gamma'(t)|dt$
can someone direct me? Thank you.