Mathematica to recognize e−iθ as the eulers identity

[arierreF]

I just need to know how can Mathematica recognize $e^{-i\theta}$ as the eulers identity. This is, $e^{-i\theta} = cos \theta + sin \theta$.


When i plot a function like $e^{i\theta}$, nothings appear in the graph.

Help is appreciated.

 

[MednataMiza]

You can use something fancy like this:

Plot[Im@Exp[-I x], {x, -5, 5}, PlotStyle -> Thick, 
 ColorFunction -> "StarryNightColors"]

 

[arierreF]

Thanks it works!