SummaryThis paper deals with certain aspects of complex geometry. Our field of study, which we have calledhyperanalytic geometry, is concerned with two problems:the geometrical representation of complex functions of a single complex variable, andthe geometric properties of these representations.In Section 1, a graphical basis is constructed for a complex hyperanalytic geometry of four dimensions. This analytic geometry is used in Section 2 to obtain graphs of some elementary complex functions. The complex line and the complex circle are examined in detail. In Section 3, the hyperanalytic model is applied to resolve some present paradoxes in complex geometry.