I want to get a cosine from taking the real part of a complex exponential: $cos(x) = Re(exp(i x))$. What I do in Mathematica is
(1/2)*(Exp[x*I] + Conjugate[Exp[x*I]]) // TraditionalForm // FullSimplify
but this gives me
1/2 (E^(-I x^\[Conjugate]) + E^(I x)) instead of
cos(x). Why is that?