Lost in the mystery of $\large e^{i \pi } + 1$

$1+ e^{\large -\frac{180^\circ}{i}}$

$= 1+ e^{\large -\frac{\pi}{i}}$

$= 1 + e^{\large -\frac{\pi(-i)}{i(-i)}}$ $~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~$ $;\left[\text{Multiply by} \dfrac{-i}{-i}\right]$

$= 1 + e^{\large -(-\pi i)}$

$= 1 + e^{\large \pi i}$

$= 1- 1$

$= \boxed{0}$

$\large 1 + e^{- \frac{180 °}{i}}$ = $\large e^{i \pi } + 1$

$\therefore \implies = 0$