Mathematica 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!