Lesson 15

Working Backwards

Lesson Narrative

In this lesson, students bring together what they have learned so far about complex numbers and arithmetic operations on them. The main activity is an Information Gap where students must ask for the information they need to find the real and imaginary parts of complex numbers that have been multiplied, requiring them to use precise language as they work with their partner (MP6).

Learning Goals

Teacher Facing

• Determine what information is needed to find the complex numbers that were multiplied to get a certain result, and ask questions to elicit that information.

Student Facing

Let's use what we've learned about multiplying complex numbers.

Required Preparation

In the Information Gap activity, prepare the third pair of cards to use if time allows for an additional more challenging problem.

Student Facing

• I can find real and imaginary parts of complex numbers if I know enough about the numbers and their product.

Building On

Building Towards

Glossary Entries

• complex number

A number in the complex plane. It can be written as $$a + bi$$, where $$a$$ and $$b$$ are real numbers and $$i^2 = \text-1$$.

• imaginary number

A number on the imaginary number line. It can be written as $$bi$$, where $$b$$ is a real number and $$i^2 = \text-1$$.

• real number

A number on the number line.