"Complex numbers: a methodological guide for self-study" is a unique educational resource created by a team of authors, which opens up to the reader a fascinating world of complex numbers and their infinite possibilities. This book will become an indispensable assistant for students, teachers and anyone who wants to understand and master one of the most important sections of mathematics, which are the basis of modern science and technology. The focus of this book is the concept of complex numbers, their properties, operations and applications in various fields. The authors masterfully reveal complex topics, turning them into understandable and accessible for self-study. The book explains in detail the basics of algebraic and geometric aspects of complex numbers, introduces the concepts of a module, an argument, a complex plane and a trigonometric form. Particular attention is paid to practical tasks and exercises, which makes the manual not only theoretical, but also as applied as possible. The reader will be able to independently go from simple arithmetic operations to complex problems associated with the use of complex numbers in engineering calculations, physics and computer science. This book is intended for a wide range of readers - from high school students and first-year students to teachers looking for an effective tool for learning. It is especially suitable for those who appreciate clarity of presentation, a systematic approach and a practical focus. The age audience is from 16 years and older, and interest in mathematics and the desire to understand complex concepts make it relevant for those who strive for in-depth mastery of the subject. What makes "Complex numbers: a methodical manual for self-study" special? First of all, the author's style, combining the rigor of the scientific approach with a living, understandable language . The team of authors uses many illustrations, diagrams and examples to show how complex numbers work in real life and scientific tasks. The book raises topics important for modern education and professional activity - from solving equations and analyzing functions to the use of complex numbers in electronics, quantum mechanics and computer graphics. Special attention is paid to the development of skills of independent search for solutions, critical thinking and analytical approach. The authors do not just give theoretical definitions, but show how to apply knowledge in practice, solving real problems. This approach makes the book not only a textbook, but also an incentive to develop logical thinking and a creative approach to mathematics. If you are looking for a book that will help you understand and master complex numbers from scratch or deepen your existing knowledge, then this guide is exactly what you need. It is suitable for those who appreciate a systematic approach, want to learn how to apply mathematics in life and professional activities, as well as for teachers looking for modern and understandable material for their students. The author's team, known for his other works on mathematics and pedagogy, created a book that not only explains complex topics, but also inspires further study. The style of presentation combines scientific rigor with a lively, motivating language, which makes the book attractive to a wide range of readers. In general, “Integrated Numbers: A Methodical Guide for Self-Study” is not just a textbook, but a real journey into the amazing world of complex numbers, revealing their secrets and possibilities, which can become a reliable companion on the way to mathematical mastery.