Lessons 36–40 provide students with the necessary tools to find solutions to polynomial equations outside the realm of the real numbers. This lesson illustrates how to both analytically and graphically identify a system of equations that has no real number solution. In the next lesson, the imaginary unit 𝑖 is introduced, and students begin to work with complex numbers through the familiar geometric context of rotation.
Students realize that the set of complex numbers inherits the arithmetic and algebraic properties from the real numbers. The work with complex solutions to polynomial equations in these lessons culminates with the fundamental theorem of Algebra in Lesson 40, the final lesson in this module.
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