The coupling between an inductive source and the plasma determines the power transfer efficiency and the reflected impedance in the primary circuit. Usually, the plasma coupling is analysed by means of a transformer equivalent circuit, where the plasma inductance and resistance are estimated using a global plasma model. This paper shows that, for planar RF antennas, the mutual inductance between the plasma and the primary circuit can be calculated using partial inductances and the complex image method, where the plasma coupling is determined in terms of the plasma skin depth and the distance to the plasma. To introduce the basic concepts, the mutual inductance is calculated here for a linear conductor parallel to the plasma surface. In the accompanying paper part II Guittienne et al (2015 Plasma Sources Sci. Technol. 24 065015), impedance measurements on a RF resonant planar plasma source are modeled using an impedance matrix where the plasma-antenna mutual impedances are calculated using the complex image method presented here.