7 The complex number \(- 2 + \mathrm { i }\) is denoted by \(u\).
- Given that \(u\) is a root of the equation \(x ^ { 3 } - 11 x - k = 0\), where \(k\) is real, find the value of \(k\).
- Write down the other complex root of this equation.
- Find the modulus and argument of \(u\).
- Sketch an Argand diagram showing the point representing \(u\). Shade the region whose points represent the complex numbers \(z\) satisfying both the inequalities
$$| z | < | z - 2 | \quad \text { and } \quad 0 < \arg ( z - u ) < \frac { 1 } { 4 } \pi$$