
theorem Th44:
  for n being non zero Element of NAT for x being Real ex y being
Element of F_Complex st y = x & eval(unital_poly(F_Complex,n),y) = (x |^ n) - 1
proof
  let n be non zero Element of NAT, x be Real;
  x in COMPLEX by XCMPLX_0:def 2;
  then reconsider y=x as Element of F_Complex by COMPLFLD:def 1;
  ex x2 being Real st x2 = y & (power F_Complex).(y,n) = x2 |^ n by Th43;
  then eval(unital_poly(F_Complex,n),y) = (x |^ n) - 1 by Th41;
  hence thesis;
end;
