A small manufacturing plant is located \(2 \mathrm{~km}\) down a transmission line, which has a series reactance of \(0.5 \Omega / \mathrm{km}\). The line resistance is negligible. The line voltage at the plant is \(480 / 0^{\circ} \mathrm{V}\) (rms), and the plant consumes \(120 \mathrm{~kW}\) at 0.85 power factor lagging. Determine the voltage and power factor at the sending end of the transmission line by using

(a) a complex power approach and

(b) a circuit analysis approach.