Education Technology

Pythagoras is not Real

Published on 07/18/2017

Activity Overview

Students manipulate the location of z on the Argand plane and observe the location of z squared on a second Argand plane. The coefficients of z squared form the two shorter sides of a right angled Pythagorean triangle. Students explore this relationship then prove it. The extension activity includes the opportunity to explore the polar form of a complex number in an informal manner.

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

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.