Lossless networks with imaginary-valued resistances of one sign

The problem of characterizing lossless electrical networks composed of either capacitors or inductors and imaginary-valued resistors whose resistance is of one sign is solved. The impedance (and admittance) singularities are all on one-half the imaginary-frequency axis. The results are related to analogous results for RC and LC networks. These results are of significance in fields using such networks as motors, electric circuits, and narrow-band carrier circuits. It is a generalization of Foster's Reactance Theorem.