Objectives
- Square imaginary numbers (rectangular form)
- Work with real and imaginary components
- Informal exploration of Polar form
Vocabulary
- Argand Plane
- Real component
- Imaginary component
- Magnitude / Modulus
- Angle / Argument
About the Lesson
Watch Activity Tutorial
Students manipulate z plotted on the Argand plane, the corresponding value of z squared is plotted on an adjacent Argand plane. If the real and imaginary components of z are integer quantities then the real and imaginary components of z squared form the shorter side lengths of a Pythagorean triple. After identifying a collection of triples, students are required to prove that this will always work.
An extension activity allows students to also informally explore the polar form of a complex number.