reserve x for Real;

theorem
  for x be Element of COMPLEX for n be non zero Nat for k be Nat holds
(n-root |. x .|)*cos((Arg x+2*PI*k)/n)+ (n-root |. x .|)*sin((Arg x+2*PI*k)/n)*
  <i> is CRoot of n,x
proof
  let x be Element of COMPLEX;
  let n be non zero Nat;
  let k be Nat;
  reconsider z = (n-root |. x .|)*cos((Arg x+2*PI*k)/n)+ (n-root |. x .|)*sin(
  (Arg x+2*PI*k)/n)*<i> as Element of COMPLEX by XCMPLX_0:def 2;
  z|^n = x by Th56;
  hence thesis by Def2;
end;
