Trigonometry system - complex conjugate

Question

I have the following function $$e_n(t) = e^{2\pi int}, t \in R, n \in Z$$ Could anyone explain how one can go from this: $$e_m(t) \bar e_n(t) $$ to $$e^{-2\pi i(m - n)t}$$

Shouldn't it be $e^{2\pi i(m - n)t}$ instead of $e^{-2\pi i(m - n)t}$?

Answer 1

If $e_n(t)=e^{2πint}$, the conjugate is $\bar{e}_n(t)=e^{-2πint}$

Then

$e_m(t)\bar{e}_n(t)=e^{2πimt}e^{-2πint}=e^{-2πi(n-m)t}.$