Hi, I'm trying to do some simple computations with 7th roots of unity that fail. I define
m=Exp[2Pi I/7]
and then, as a sanity check, I ask Mathematica to check that 1+m+...+m^6=0, but I don't see how to get this done.
Simplify[Sum[m^k,{k,0,6}]]
does not work.
For the record, I also tried the analogous thing when m=Exp[2Pi I/5], and it also failed. But it did work when I defined
m=Cos[2Pi/5]+I*Sin[2pi/5]
