3 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 \(z ^ { * }\), the complex conjugate of \(z\).
- Find, in terms of \(x\) and \(y\), the real and imaginary parts of
$$2 z - \mathrm { i } z ^ { * }$$
- Find the complex number \(z\) such that
$$2 z - \mathrm { i } z ^ { * } = 3 \mathrm { i }$$