# Lesson 14

More Arithmetic with Complex Numbers

### Lesson Narrative

This lesson is optional because it is an opportunity for extra practice that not all classes may need.

In this lesson, students practice using complex number arithmetic to write expressions in the form $$a+bi$$, where $$a$$ and $$b$$ are real numbers. Students look for and make use of repeated reasoning to analyze the expression $$i^n$$, where $$n$$ is a whole number (MP8). They also construct viable arguments and critique the reasoning of others when they resolve discrepancies during a row game (MP3).

### Learning Goals

Teacher Facing

• Add, subtract, and multiply complex numbers, and represent the solutions in the form $a+bi$.
• Explain reasoning and critique the reasoning of others when writing numbers in the form $a+bi$.
• Generalize patterns in repeated reasoning to show what happens when $i$ is raised to different powers.

### Student Facing

• Let’s practice adding, subtracting, and multiplying complex numbers.

### Student Facing

• I can do arithmetic with complex numbers.

### 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 $$i^2 = \text-1$$.

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