A balanced $3$ phase load is connected in a star configuration, developing an output of $12$M W with an efficiency of $90\%.$ The load is supplied with $3$ phase at $50$Hz via a line with impedance Z$1$ of $(0\mathrm{.}3+$ j$0\mathrm{.}5)$ per phase. The power factor is $0\mathrm{.}82$ lagging and the voltage at the load is exactly $10$kV line to line. Calculate: $($a$)$ the line current in complex number form. $(5$ marks$)($b$)$ the impedance of the load. $(4$ marks$)($c$)$ the magnitude of the line voltage at the supply. $(5$ marks$)($d$)$ the amount of the true and reactive power drawn from the supply. $(5$ marks$)($e$)$ the amount of power correcting Vars needed to improve the power factor to $0\mathrm{.}9$