Simple explanation needed for exponential

Question

While going through my professor's notes while calculating integral with branch cut, I came across this relation.It's basic,I guess.So,How this relation come from $e^{i\frac{3\pi}{4}}=e^{-i\frac{\pi}{4}}$

Answer 1

That relation is wrong. $$ e^{3\pi i/4}e^{\pi i/4} = e^{\pi i} = -1 $$ whereas $$ e^{-\pi i/4}e^{\pi i/4} = 1 $$

Answer 2

It is not correct. We do have that $e^{2\pi i}=1=e^0$, and then it follows that, $\forall a,e^{a}=e^{a}\cdot 1=e^ae^{2\pi i}=e^{a+2\pi i}$, but what you're saying isn't true.