A transformer has self-inductances \(L_{1}=200 \mathrm{mH}, L_{2}=\) \(200 \mathrm{mH}\), and a coupling coefficient of \(k=0.5\). The transformer is operating in the sinusoidal steady state with \(\omega=500 \mathrm{rad} / \mathrm{s}\) and a \(50-\Omega\) resistive load connected across the secondary winding. Find the transformer input impedance. Assume additive coupling.