Calculate Exp[2*n* Pi*I] treating n as Integer?

Questions
1

I want to ask Mathematica to evaluate

Exp[2*n* Pi*I]

treating n, as Integer. the answer is 1, but Mathematica writes

Cos[2nPi]+I Sin[2n PI]

so how to force n to be treating n as Integers?
Thanks.
JME

2

Here is one way:

In[2]:= Simplify[Exp[2 n Pi I], n \[Element] Integers]

Out[2]= 1