First, students will learn how to multiply a complex number by a real number. They'll learn how to do this algebraically, and how to interpret it graphically. Next, students will learn how to multiply complex numbers algebraically. After that, students will learn how to multiply complex numbers graphically. Three excellent videos are here, here, and here. Before attempting this section, students must know how to multiply binomials with variables. They must also know how to find the argument and modulus of a complex number, and that \(i^2 = -1.\)
Provide a Desmos interactive.
Multiplying complex numbers by Khan Academy
Conclude by giving your students these challenges:
2021 Math Kangaroo Levels 9-10 Problem #22: If \(a + b + c = 0\) and \(abc = 78,\) what is the value of \((a + b)(b + c)(c + a)?\) Here's the solution.