In the introductory part of this paper, we addressed complex numbers, algebraic structures, and Euclid’s plane geometry studied in many separate teaching disciplines at many of the faculties that prepare future teachers of mathematics. At that, as we can see from the aims that need to be achieved while studying the mentioned content we have minimal integration of content studied with complex numbers and Euclid’s plane geometry. Further in this paper we will present program content that can significantly improve integration of teaching, and also improve the training of future mathematics teachers. Also, we can achieve the last with the introduction of a new teaching course Geometry of complex numbers, as well as with the study of the mentioned content within the existing courses in elementary mathematics found at the majority of faculties that prepare mathematics teachers. Faculties that train future mathematics teachers, without any exception, have the subject geometry, most frequently, with the following syllabus: