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).
Lesson overview
 14.1 Warmup: Which One Doesn’t Belong: Complex Expressions (5 minutes)

14.2 Optional Activity: Powers of \(i\) (15 minutes)
 Includes "Are you Ready for More?" extension problem
 14.3 Optional Activity: Add 'Em Up (or Subtract or Multiply) (15 minutes)
 Lesson Synthesis
 14.4 Cooldown: Operate on Complex Numbers (5 minutes)
Learning goals:
 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.
Learning goals (student facing):
 Let’s practice adding, subtracting, and multiplying complex numbers.
Learning targets (student facing):
 I can do arithmetic with complex numbers.
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