Education Technology

# Activities

• ##### Subject Area

• Standard: VCE: Specialist Mathematics: Specialist Mathematics

Aust Senior

25 Days

• ##### Device
• TI-Nspire™ CX
• TI-Nspire™ CX CAS
• TI-Nspire™ Apps for iPad®
• ##### Software

TI-Nspire™
TI-Nspire™ CAS
TI-Nspire™ Navigator™ NC System
TI-Nspire™ CAS Navigator™ NC System

4.4

## Pythagoras is not Real

#### 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

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.