reserve x,y for Real;
reserve z,z1,z2 for Complex;
reserve n for Element of NAT;

theorem
  for n being Element of NAT, z being Element of COMPLEX holds exp(<i>*n
  *z) = (cos_C/.z + <i>*sin_C/.z) |^ n
proof
  let n be Element of NAT;
  let z be Element of COMPLEX;
  exp(<i>*n*z) = exp(<i>*(n*z)) .=cos_C/.(n*z) + <i>*sin_C/.(n*z) by Th36;
  hence thesis by Th50;
end;
