The paper researches methodical aspects by a statement of the complex analysis at lectures and a practical training with students of the engineering directions. The features of teaching connected with consideration of applied problems of complex analysis for various physical appendices. The features of perception of a course by students are noted. Forms of control of student's knowledge are offered. Affected by the historical aspect of the complex analysis development as a science and recommended methodologically justified way of presenting difficulties for the perception of the material. Special attention is paid to the subject of the first lecture in this course. Methodical recommendations for the teachers, leading workshops, are given. It is recommended to train students adhering to the three major principles: the principle of analog modeling of the content, the principle of local integration systematization of the knowledge of students and the principle of the illustrations of the concepts and methods of the analytical functions theory on physics and technology examples. The example of the test, to check the student's knowledge of definitions and properties of the objects of study of complex analysis , consisting of ten tasks with multiple choice, is given.