Complex Numbers and Transformation Geometry - February 2007, Stage 4&5

Problems

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Arrow Arithmetic 1

Stage: 4 Challenge Level: Challenge Level:1

The first part of an investigation into how to represent numbers using geometric transformations that ultimately leads us to discover numbers not on the number line.

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Arrow Arithmetic 2

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Introduces the idea of a twizzle to represent number and asks how one can use this representation to add and subtract geometrically.

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Arrow Arithmetic 3

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

How can you use twizzles to multiply and divide?

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Root Tracker

Stage: 5 Challenge Level: Challenge Level:1

Track the roots of quadratic equations as you move the corresponding graphs and discover the transitions from real to complex roots.

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Conjugate Tracker

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Make a conjecture about the curved track taken by the complex roots of a quadratic equation and use complex conjugates to prove your conjecture.