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 Th39:
  for c being Complex
  for s being Real holds Rotate(c,s) = Rotate(c,s+2*PI*i)
  proof
    let c be Complex;
    let s be Real;
    cos (s+Arg c) = cos (s+Arg c+2*PI*i) &
    sin (s+Arg c) = sin (s+Arg c+2*PI*i) by COMPLEX2:8,9;
    hence thesis;
  end;
