Loop statement inside an Exponential

Questions
1

I’m trying to write a loop statement in Mathematica so that I get the output that looks a little something like this:
{ 1, Exp[-I*2*Pi/5], Exp[-I*2*Pi*2/ 5], Exp[-I*2*Pi*3/5], Exp[-I*2*Pi*4/5, …}.

Does anybody know what I must do to get it to give a simliar output above? The output doesn’t have to be exact; it can be in aproximate form (real part + imaginary part).

Thank you in advance.

k = 1;
A = 5;
a0 = 0;
a0 = a;
n = 4;
F0 = 0;
Do[ F =  F - I*2*Pi*k*(a)/(A); Print[Exp[F]], {i, 0, n}]
2 
In[1]:= k = 1;
A = 5;n = 4;
Table[If[i==0, "1", StringReplace["Exp[-I*2*Pi*k*z]", "z"->ToString[InputForm[i/A]]]], {i, 0, n}]

Out[4]= {1, Exp[-I*2*Pi*k*1/5], Exp[-I*2*Pi*k*2/5], "Exp[-I*2*Pi*k*3/5], Exp[-I*2*Pi*k*4/5]}

Will that do? It is producing strings to try to match your format exactly.

If you then need to use this result for further calculations then ToExpression can convert it back.

3

Thanks, Bill. Now I have to take the Output and apply to a Discrete Fourier Tranform.

4

If you are only using this for calculations and don’t care about the exact formatting then this might be simpler

In[4]:= k = 1;A = 5; n = 4;Table[Exp[-I*2*Pi*k*i/A], {i, 0, n}]

Out[6]= {1, E^(-((2 I \[Pi])/5)), E^(-((4 I \[Pi])/5)), E^((4 I \[Pi])/5), E^((2 I \[Pi])/5)}