reserve a, b, c, d, x, y, z for Complex;

theorem Th27:
  x.|.y = (Re x)*(Re y)+(Im x)*(Im y) + (-(Re x)*(Im y)+(Im x)*(Re y))*<i>
proof
  x = Re x+(Im x)*<i> & y*' = Re y-(Im y)*<i> by COMPLEX1:13,def 11;
  hence thesis;
end;
