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Deep connections between complex numbers and geometry had been well known and carefully studied centuries ago. Fundamental objects that are investigated are the complex plane (usually extended by a single infinite point), its objects (points, lines and circles), and groups of transformations that act on them (e.g., inversions and Möbius transformations). In this paper, we treat the geometry of complex numbers formally and present a fully mechanically verified development within the theoremdoi:10.1007/s10472-014-9436-4 fatcat:vfc4c5y6ufgovglq2r2jlvkzbm