- Given that
$$\frac { 3 z - 1 } { 2 } = \frac { \lambda + 5 i } { \lambda - 4 i }$$
where \(\lambda\) is a real constant,
- determine \(z\), giving your answer in the form \(x + y i\), where \(x\) and \(y\) are real and in terms of \(\lambda\).
Given also that \(\arg z = \frac { \pi } { 4 }\)
- find the possible values of \(\lambda\).