6 It is given that \(z = x + \mathrm { i } y\), where \(x\) and \(y\) are real numbers.
- Write down, in terms of \(x\) and \(y\), an expression for
$$( z + \mathrm { i } ) ^ { * }$$
where \(( z + \mathrm { i } ) ^ { * }\) denotes the complex conjugate of \(( z + \mathrm { i } )\).
- Solve the equation
$$( z + \mathrm { i } ) ^ { * } = 2 \mathrm { i } z + 1$$
giving your answer in the form \(a + b \mathrm { i }\).