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An Introduction to Complex Numbers

A short introduction to complex numbers written primarily for students aged 14 to 19.

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Cube Roots

Evaluate without a calculator: (5 sqrt2 + 7)^{1/3} - (5 sqrt2 - 7)^1/3}.

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Root Tracker

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

Complex Rotations

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

Possible extension

Try multiplying by $e^{{i\pi \over 3}} = {1\over 2} + i{\sqrt 3 \over 2}.$