Parallel conjugate impedances
= Parallel conjugate impedances
{title2=$Z_\parallel=R(1+s^2)/2$}
Two parallel branches with <complex impedances> $R(1+is)$ and $R(1-is)$ have a real input impedance $R(1+s^2)/2$, since their admittances have cancelling imaginary parts. For $s=\sqrt{15}$, adding a series resistance $2R$ gives total impedance $10R$. With source voltage amplitude $V_0$, each branch-resistor drop and the series-resistor drop has amplitude $V_0/5$, despite their different <phases>.