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. Full lesson plan (warm-up, activities, synthesis, cool-down prompt) from Alg2.3 Complex Numbers and Rational Exponents, Algebra 2.