\( \omega \) is a complex cube root of unity and \( Z \) is a complex number satisfying \( |Z-1| \le 2 \). The possible values of \( r \) such that \( |Z-1| \le 2 \) and \( |\omega Z - 1 - \omega^2| = r \) have no common solution are
Show Hint
Always simplify complex equations like \( |\omega Z + \dots| \) by factoring out \( |\omega| \) to reveal the standard circle form \( |Z - z_0| = r \). Drawing a diagram with centers and radii often makes the intersection conditions obvious.