(i) To find w², calculate \((2 + i)^2\):

\((2 + i)^2 = 2^2 + 2 \cdot 2 \cdot i + i^2 = 4 + 4i + i^2\).

Since \(i^2 = -1\), this becomes \(4 + 4i - 1 = 3 + 4i\).

The modulus of w² is \(|3 + 4i| = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5\).

(ii) On an Argand diagram, the region is a circle centered at \((3, 4)\) with radius 5, representing the inequality \(|z - w^2| \leq |w^2|\).