3 The complex number \(w\) is defined by \(w = 2 + \mathrm { i }\).
- Showing your working, express \(w ^ { 2 }\) in the form \(x + \mathrm { i } y\), where \(x\) and \(y\) are real. Find the modulus of \(w ^ { 2 }\).
- Shade on an Argand diagram the region whose points represent the complex numbers \(z\) which satisfy
$$\left| z - w ^ { 2 } \right| \leqslant \left| w ^ { 2 } \right|$$