6 Throughout this question the use of a calculator is not permitted.
The complex number \(2 - \mathrm { i }\) is denoted by \(u\).
- It is given that \(u\) is a root of the equation \(x ^ { 3 } + a x ^ { 2 } - 3 x + b = 0\), where the constants \(a\) and \(b\) are real. Find the values of \(a\) and \(b\).
- On a sketch of an Argand diagram, shade the region whose points represent complex numbers \(z\) satisfying both the inequalities \(| z - u | < 1\) and \(| z | < | z + \mathrm { i } |\).