Use smith chart method to design an L$-$section matching network to match a load with an impedance ZL $=8+$ j $12$ W to a transmission line of characteristic impedance Zo $=40$ W at a generator frequency of $1000$ MHz$.$ Then answer the questions from $1$ to $8$:

$$

$1.$ Z$1=$

$2.$ Z$2=$

$3.$ jX$1=$

$4.$ jX$2=$

$5.$ Y$1=$

$6.$ Y$2=$

$7.$ jB$1=$

$8.$ jB$2=$

provide calculation and smith chart with graphical solution.