[QUE/QM-06108]

 A particular state of a physical system is represented by \[\psi = \begin{pmatrix}  1 \\ 1+i \\ 1-i \end{pmatrix}.\] Find value of \(\lambda\) such that the vector \(\phi\), where \[ \phi= \begin{pmatrix} \lambda \\ 2i \\ 2\end{pmatrix}\] may represent the same state as \(\psi\).
\paragraph*{Answer: \(\lambda = (1+i)\)}