10 The complex number \(- 1 + \sqrt { 7 } \mathrm { i }\) is denoted by \(u\). It is given that \(u\) is a root of the equation
$$2 x ^ { 3 } + 3 x ^ { 2 } + 14 x + k = 0$$
where \(k\) is a real constant.
- Find the value of \(k\).
- Find the other two roots of the equation.
- On an Argand diagram, sketch the locus of points representing complex numbers \(z\) satisfying the equation \(| z - u | = 2\).
- Determine the greatest value of \(\arg z\) for points on this locus, giving your answer in radians.
If you use the following lined page to complete the answer(s) to any question(s), the question number(s) must be clearly shown.