7 The complex number \(2 + 2 \mathrm { i }\) is denoted by \(u\).
- Find the modulus and argument of \(u\).
- Sketch an Argand diagram showing the points representing the complex numbers 1, i and \(u\). Shade the region whose points represent the complex numbers \(z\) which satisfy both the inequalities \(| z - 1 | \leqslant | z - \mathrm { i } |\) and \(| z - u | \leqslant 1\).
- Using your diagram, calculate the value of \(| z |\) for the point in this region for which \(\arg z\) is least.