Remote protection is the basic protection of high-voltage transmission networks, which are mostly complex and looped and fed from several sides. The operating time of remote protection depends on the distance of the installation point of the remote relay from the location of the fault. The remote relay is connected to the current and voltage transformers, so it measures the current and voltage and determines the impedance based on their ratio. Argand’s diagram, k-circles, ψ-circles, orthogonal trajectories and conformal mapping, mathematical expressions that are useful for any type of protective devices and are also necessary for remote relays, are analyzed in this thesis. For the analysis of the measured impedance, fictitious substitute systems were used to show the occurrences of phase-to-phase short-circuits and short-circuits to earth. Interphase short circuits include three-pole and two-pole short circuits, while short circuits with earth include single-pole short circuits and two-pole short circuits with simultaneous earth connection. The most adequate way of observing the measured impedance seen by the relay at the place of installation of the relay device is the graphical representation of the impedance in the complex Argand plane.