reserve i,j for Element of NAT,
  x,y,z for FinSequence of COMPLEX,
  c for Element of COMPLEX,
  R,R1,R2 for Element of i-tuples_on COMPLEX;

theorem Th23:
  for z being Complex holds z-z*' = 2*(Im z) * <i>
proof
  let z be Complex;
  z-z*'= Re z - Re (z*') + (Im z - Im (z*'))*<i> by COMPLEX1:84
    .= Re z - Re (z*')+(Im z - -Im z)*<i> by COMPLEX1:27
    .= Re z - Re z + (Im z - -Im z)*<i> by COMPLEX1:27
    .= 2*(Im z)*<i>;
  hence thesis;
end;
