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
$$\mathrm { i } ( z + 7 ) + 3 \left( z ^ { * } - \mathrm { i } \right)$$
- Hence find the complex number \(z\) such that
$$\mathrm { i } ( z + 7 ) + 3 \left( z ^ { * } - \mathrm { i } \right) = 0$$