3 It is given that \(z = x + \mathrm { i } y\), where \(x\) and \(y\) are real numbers.
- Find, in terms of \(x\) and \(y\), the real and imaginary parts of
$$z - 3 \mathbf { i } z ^ { * }$$
where \(z ^ { * }\) is the complex conjugate of \(z\).
- Find the complex number \(z\) such that
$$z - 3 \mathrm { i } z ^ { * } = 16$$