8 Throughout this question the use of a calculator is not permitted.
The complex number \(u\) is defined by
$$u = \frac { 4 \mathrm { i } } { 1 - ( \sqrt { } 3 ) \mathrm { i } }$$
- Express \(u\) in the form \(x + \mathrm { i } y\), where \(x\) and \(y\) are real and exact.
- Find the exact modulus and argument of \(u\).
- On a sketch of an Argand diagram, shade the region whose points represent complex numbers \(z\) satisfying the inequalities \(| z | < 2\) and \(| z - u | < | z |\).