Problem $2(50$ points$)$ For the two bus power system shown in following figure, solve the following problems using the Newton$-$Raphson $(N-R)$ method $($flat start: ${}_2=0,|V_2|=1\mathrm{.}0)$

$($a$)(10$ points$)$ Calculate $Z_{\text{b}\text{u}\text{r}}$

$($b$)(20$ points$)$ Find the Jacobian matrix $($J$)$ for a load flow calculation

$($c$)(20$ points$)$ Calculate ${}_2($degree$)$ and $|V_2|($pu$)$ after the third iteration using a flat start