In your Table you should use E to get the exponential function.
And you may want to have a look at this
n = 5; mat = Table[(E^(2 I Pi/n))^(i*j), {i, 0, n - 1}, {j, 0, n - 1}]; dd = Det[mat] dd1 = dd /. a_. Exp[b_ Complex[0, x_] ] -> a (Cos[x b] + Im Sin[x b]) dd1 // Expand dd // FullSimplify
Use E instead of e?
In[1]:= n=4; mat=Table[(E^(2 I Pi/n))^(i*j), {i, 0, n-1}, {j, 0, n-1}] Out[2]= {{1,1,1,1},{1,I,-1,-I},{1,-1,1,-1},{1,-I,-1,I}}
Worked like a charm. Thank you!
