Problem $1$: A certain transmission line $2$m long operating at $=$ rad$/$s has an attenuation constant of $=/$ and a phase constant of $=$ rad$/$m$.$ The characteristic impedance of the T$-$line is $=+.$ If the line is connected to a source $=$ V$,$ with a source impedance of $=,$ and is terminated by a load of $=+,$ calculate:

$($a$)$ The input impedance $()$

$($b$)$ The sending$-$end current

$($c$)$ The current at the middle of the line

$($d$)$ The voltage reflection coefficient

$($e$)$ The average power injected into the T$-$line $($f$)$ The voltage standing wave ratio.