 Solution

Use the phasor convention $v(t)=\mathrm{Re}(\tilde{V}{e}^{i\omega t})$. The complex impedance is $Z=\tilde{V}/\tilde{I}$ in sinusoidal steady state. From $v_R=Ri$, $i_C=Cd{v}_C/dt$, and $v_L=Ld{i}_L/dt$,For this convention an ideal inductor has voltage leading current by $\pi /2$, while an ideal capacitor has current leading voltage by $\pi /2$.