Complex Numbers: Definitions and Operations

This lecture introduces the topic of complex numbers, discussing their historical background, theoretical aspects, and applications in mathematics and engineering. The instructor explains the definition of a complex number and its Cartesian form, emphasizing the theoretical nature of the lesson. The lecture covers the introduction of the imaginary unit 'i' and its properties, including the concept of conjugation. It explores the significance of complex numbers in solving algebraic equations and demonstrates operations such as addition, multiplication, and conjugation. The lecture concludes with a discussion on powers and roots of complex numbers, illustrating how to calculate square roots of complex numbers through a systematic approach.