= Solution
Let the unknown <series circuit> contain <electrical resistance> $R_s>0$ and <inductance> $L>0$. Its <electrical impedance> is $Z=R_s+i\omega L$. Thus $A=R_s$, $B=L$, and conjugate <impedance matching> is possible with
$$
\boxed{R=R_s,\qquad \omega=\frac1{\sqrt{LC}}.}
$$
At this <angular frequency>, the <inductor> and load <capacitor> have opposite <electrical reactances> of equal magnitude. Literal equality of their separate <electrical impedances> is impossible; for example, $R_s=L=C=1$ gives $1+i\omega$ versus $R-i/\omega$ for every $\omega>0$.
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