I'm reading a lemma's proof, and the proof starts with:
Let $\alpha \in \text{arg}(\int^b_af(t)dt)$: $$ \Bigg|\int^b_af(t)dt\Bigg|=e^{-i \alpha}\int^b_af(t)dt $$
I know that $z=r\cdot e^{i\alpha}$ and $|z|=r$, but idk how to related those things to the previous equation.
If $z=r\cdot e^{i\alpha}$ then $e^{-i\alpha}z=e^{-i\alpha}\cdot r\cdot e^{i\alpha}=r(e^{-i\alpha}e^{i\alpha})=re^{-i\alpha+i\alpha}=re^0=r=|z|.$