After working on De Moivre’s Theorem in yesterday’s lesson, it is a good idea to begin today’s lesson by recapping the important information about the theorem. I find that students need this second explanation of the concepts. While it will not be as in-depth as yesterday, students will need to revisit these concepts to cement them in their minds. Here are some questions you can ask to get them thinking about the theorem.
1. What is De Moivre’s Theorem?
2. What type of problems did you use it for in yesterday’s homework?
3. How does it relate to trigonometric form of complex numbers?
4. When you raise a complex number to a power, what are the steps you have to do to get your answer?
As I mentioned in yesterday’s narrative, questions #3e and #4 on the homework are ones that usually give my students trouble, so I would recommend that you talk about these with your class, even if they do not ask about them. Have a student volunteer show their work on the document camera and explain how they got their solution.
Here is the exam review that I give my students for this unit. It is nice to give them an extended amount of time to work on these problems in class so that they can bounce ideas off of their tables and they can ask questions from you if needed. I will usually give them a handout with the answers on it so they can check their work as they go. If they don’t get the correct answer, they can ask someone right away to get instant feedback.
Questions that my students almost always ask about are #3, #4, and #5. In the video below I give some tips on these questions and some issues you might want to look out for.