reserve x,y,z for Real,
  a,b,c,d,e,f,g,h for Nat,
  k,l,m,n,m1,n1,m2,n2 for Integer,
  q for Rational;

theorem Th1:
  for x being Complex holds x|^2=x*x & (-x)|^2=x|^2
proof
  let x be Complex;
A1: (-x)|^1=-x;
A2: x=x|^1;
  then x|^(1+1)=x*x by NEWTON:8;
  then x|^2=(-x)*(-x) .=(-x)|^(1+1) by A1,NEWTON:8;
  hence thesis by A2,NEWTON:8;
end;
