# Review of Polynomial Roots and Complex Numbers

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## Objective

SWBAT put together what they have learned about polynomials roots and complex numbers.

#### Big Idea

Arithmetic with polynomials and complex numbers are performed in similar ways, but powers of i have a meaning distinct from powers of variables.

## Warm-Up

15 minutes

For homework, students completed Complex Numbers Intro, which was a substantial assignment.  As I check this assignment, I display the solutions on the overhead and ask students to mark on their packets any questions they missed.  After I check everyone's work we review the assignment to prepare for the day's review and the next day's summative assessment.

The warm up is an additional set of complex number questions - mostly about simplifying powers of i.  I send my students the formative assessment Warm-up- Simplifying Powers of i with the TI NSpire Navigator so that we can all see how the class is progressing in their ability to simplify complex expressions.

## Polynomial Roots & Complex Numbers Review

75 minutes

In this lesson, I give students a chance to put their new understanding of imaginary numbers together with what they learned earlier about polynomials.  They will be assessed on this material in a quiz the following day.

The activity Waterfall Trivia- Polynomials and Imaginary Roots is a self-advancing powerpoint with three rounds of 5 questions each.  In each round, the question is displayed for five minutes.  Students copy the problem onto a sheet of paper and work on it independently for five minutes [MP1].  They continue doing this until all 5 problems in the set have been displayed.   At the end of each round, students submit their papers to me so I can tally up the points.  The top three scorer in all three rounds win a prize, which is candy or some type of school supply.