Operations with Complex Numbers – Total Recall

The title of the lesson is scarier than the actual lesson itself. When I start this lesson I always explain to the students that they should not be scared because of the word complex. Kids are kids and the word complex will have them concerned before you even start. I have found it very helpful to address the word complex before starting the lesson.

In reality, this is actually one of the easier pre-calculus lessons for students to comprehend. Though not identical to the rules they follow with variables there are many similarities. Use this to your advantage when teaching Operations with Complex Numbers.

They will have a lot of recall and notice these similarities without you even pointing them out to them. Use this to your advantage. Let them point these similarities out to you. Don’t point them out to them (unless they really aren’t seeing them). This is a great lesson to boost their confidence. They will feel accomplished for recognizing these similarities without your pointing them out to them. Confidence goes a long way. You will notice their engagement will also go up immediately because they now feel confident to join the discussion.

I start by reviewing the Properties of Real Numbers and then show them how these imaginary and complex numbers do not fit into any of the categories of Real Numbers on a Ven Diagram. You’ll also want to touch up their rules for Simplifying Radicals and Roots and Radical Expressions. Many of the same rules apply for this lesson.