Deriving admittance matrix for shortened quarter-wavelength transmission line

For Reduced-size branch-line and rat-race hybrids for uniplanar MMIC's , how to derive equation (2) ?

and is the imaginary constant j needed in equation (1) ?

For equation (1) , I am trying to use MATLAB y2abcd() function to convert admittance matrix to ABCD matrix.

However, I am getting mismatch between MATLAB answer and actual theoretical result.

There is no help, since your questions are too easy.
This is very true for your all posts.
Always your questions are too elementary and easy to answer.

Current direction of I₂ is defined like attached figure in Y-parameter.