The figure shows a three$-$phase Y motor connected to a line$-$to$-$line voltage source $(207\mathrm{.}85$ V$)$ through a line impedance of $\backslash ((2+4\backslash$mathrm$\{$j$\})\backslash )$; the motor impedance is $\backslash (30+40\backslash$mathrm$\{$j$\}\backslash ).$

$1)$ Calculate the power factor of the circuit.

$2)$ Calculate the values of a capacitor and a resistor branch parallel to the load to improve the power factor to $0\mathrm{.}95,$ which results in minimum input current to the circuit. $($hint: Use MATLAB or similar software and set the values of $\backslash ($ R $\backslash )$ from $\backslash (1\backslash$times $10^\{-6\}\backslash )$ to $10,$ write your results in a Table form$)$