Complex Numbers: Definition

This lecture introduces complex numbers as a way to find solutions to equations that do not have solutions in the set of real numbers. By extending the number system, we can solve equations like x² = 2. The lecture covers the construction of complex numbers, their properties, and operations, such as addition and multiplication. The instructor explains how complex numbers are formed by combining real and imaginary parts, leading to the term 'complex'. The lecture also explores the algebraic rules governing complex numbers, emphasizing the significance of the new constant 'i'.