GATE Electrical 2018 | Question: 20

Question

The series impedance matrix of a short three-phase transmission line in phase coordinates is $\begin{bmatrix} Z_s & Z_m & Z_m \\ Z_m & Z_s & Z_m \\ Z_m & Z_m & Z_s \end{bmatrix}$. If the positive sequence impedance is $(1+j \: 10) \Omega$, and the zero sequence is $(4+j \: 31) \Omega$, then the imaginary part of $Z_m$ (in $\Omega$) is ___________ (up to $2$ decimal places).