reserve a,b,c,x,y,z for object,X,Y,Z for set,
  n for Nat,
  i,j for Integer,
  r,r1,r2,r3,s for Real,
  c1,c2 for Complex,
  p for Point of TOP-REAL n;

theorem
  for p being Point of TOP-REAL 2 holds
  p`1 = |.p.|*cos(Arg p) & p`2 = |.p.|*sin(Arg p)
  proof
    let p be Point of T2;
    set c = euc2cpx(p);
A1: c = |.c.|*cos(Arg c) + |.c.|*sin(Arg c)*<i> by COMPTRIG:62;
A2: |.c.| = |.p.| by EUCLID_3:25;
    Re c = p`1 & Im c = p`2 by COMPLEX1:12;
    hence thesis by A1,A2,COMPLEX1:12;
  end;
