In this video lesson, students learn how to multiply complex numbers using the definition of i and the procedures for multiplying polynomials. The lesson covers multiplying polynomials with multiple terms by a polynomial with one term, as well as multiplying two polynomials with multiple terms. Students are also introduced to the imaginary number i and how to handle i squared in complex number multiplication. By the end of the lesson, students will have a solid understanding of how to multiply any two complex numbers.