reserve a,b,c,d,a9,b9,c9,d9,y,x1,u,v for Real,
  s,t,h,z,z1,z2,z3,s1,s2,s3 for Complex;

theorem
  for z be Element of COMPLEX, n be non zero Element of NAT, k be
Element of NAT holds (n-root |.z.|)*cos((Arg z+2*PI*k)/n)+ (n-root |.z.|)*sin((
  Arg z+2*PI*k)/n)*<i> is CRoot of n,z
proof
  let z be Element of COMPLEX, n be non zero Element of NAT,k be Element of
  NAT;
  ((n-root |.z.|)*cos((Arg z+2*PI*k)/n)+ (n-root |.z.|)*sin((Arg z+2*PI*k)
  /n)*<i>)|^ n=z by Th34;
  hence thesis by COMPTRIG:def 2;
end;
