reserve a,b,c,d for Real;
reserve z,z1,z2 for Complex;

theorem
  Re(z - z*') = 0 & Im(z - z*') = 2*Im z
proof
  thus Re(z - z*') = Re z - Re (z*') by Th19
    .= Re z - Re z by Th27
    .= 0;
  thus Im(z - z*') = Im z - Im (z*') by Th19
    .= Im z - -Im z by Th27
    .= 2*Im z;
end;
