This lecture introduces the Cartesian representation of complex numbers, where a complex number is represented as a sum of a real part and an imaginary part. The lecture covers the identification of complex numbers on the complex plane, the notation for complex numbers, and the basic operations involving complex numbers. It also explains the rules for adding and multiplying complex numbers, as well as the representation of complex numbers in the Cartesian form. The lecture concludes with examples illustrating the application of these concepts in calculations.