\begin{eqnarray} \dot{Z} &=& R_{1} + j\omega L_{1} + \frac{j\omega L_{2}R_{2}}{R_{2}+j\omega L_{2}}\nonumber\\ &=& 10 + j100\pi \times \frac{1}{1000\pi} + \frac{j100\pi\times \frac{1}{100\pi}\times 3} {3+j100\pi \times \frac{1}{100\pi}}\nonumber\\ &=& 10 + j\frac{1}{10} + \frac{j3}{3+j}\nonumber\\ &=& 10 + j\frac{1}{10} + \frac{j3(3-j)}{9+1}\nonumber\\ &=& 10 + j\frac{1}{10} + \frac{3+j9}{10}\nonumber\\ &=& 10 + \frac{3}{10} + j\left(\frac{1}{10}+\frac{9}{10}\right)\nonumber\\ &=& \underline{10.3 + j}~\rm [\Omega] \end{eqnarray}