In this lesson, students are introduced to the traditional symbol to denote . Students solve various quadratic equations of the form that have imaginary solutions, and they multiply imaginary numbers together.
Students also see how the real and imaginary number lines can be used together to represent complex numbers—numbers that can be written as , where and are real numbers and . While a deep, geometric interpretation of complex numbers in the complex plane is beyond the scope of this course, some activities in this unit use the complex plane to support student understanding. The complex plane helps students conceptualize numbers that are not on the real number line and make sense of complex addition. This is similar to how the real number line can be used to understand signed numbers and signed-number addition, but is not a topic itself. There are purposefully no assessment items related to the complex plane in this course.
Students attend to precision to understand the connection between solutions to for positive , the meaning of , the imaginary numbers and , and the phrase “square roots of ” (MP6).
Learning Goals
Comprehend that the symbol means a particular square root of -1 and that an imaginary number is a real number times .
Represent solutions to equations using and the complex plane.
Student-Facing Goal
Let’s meet .
Required Preparation
None
Glossary
complex number
A number in the complex plane. It can be written as , where and are real numbers and .
Standards Alignment
Building On
6.NS.C.6
Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.
