Magnetopause is a shielding boundary of planetary magnetic field. Many mathematical models have been proposed to describe or to reproduce the magnetopause location, but they are restricted to the real-number functions. In this work, we analytically develop a magnetopause model in the complex-number domain, which is advantageous in deforming the magnetopause shape in a conformal (angle-preserving) way, and is suited to compare different models or map one model onto another.