This lesson continues to develop the idea that when complex numbers are combined, the result is also a complex number and can be written in the form , where and are real numbers. In this lesson, students use the fact that to multiply imaginary numbers, and use the strategies they develop to multiply complex numbers by writing the terms as real numbers.

Students make use of the familiar structure (MP7) of distributing terms to find the result of multiplying two complex numbers. To organize their thinking, they can use the same kind of diagrams they used in a previous unit to multiply polynomials. Students also take turns explaining their reasoning and critiquing the reasoning of others (MP3) as they match equivalent expressions: products of complex numbers and single values.