How To Multiply Complex Numbers

The Organic Chemistry Tutor

This instructional math video provides a comprehensive tutorial on multiplying complex numbers, ranging from basic imaginary units to binomials. The narrator guides viewers through a logical progression of problems, starting with simple monomials involving the imaginary unit 'i', moving to the distributive property, and advancing to the FOIL method for multiplying two complex binomials. Special attention is given to standard form (a + bi) and the properties of the imaginary unit squared. The video covers several specific scenarios that often trip up students, including multiplying square roots of negative numbers, multiplying complex conjugates, and squaring complex binomials. Through step-by-step handwritten examples on a digital blackboard, the instructor demonstrates the importance of converting negative roots to imaginary numbers before multiplying to avoid sign errors. For educators, this resource is an excellent tool for Algebra II or Pre-Calculus instruction. It serves as a clear demonstration of procedural fluency with complex numbers. Teachers can use specific segments to target common misconceptions, such as the error of multiplying radicands of negative numbers directly, or use the entire video as a review of operations within the complex number system.