Complex numbers

problem

Opening the Door

Age

14 to 18

Challenge level

What happens when we add together two complex numbers?
problem

Strolling Along

Age

14 to 18

Challenge level

What happens when we multiply a complex number by a real or an imaginary number?
problem

Napoleon's Theorem

Age

14 to 18

Challenge level

Triangle ABC has equilateral triangles drawn on its edges. Points P, Q and R are the centres of the equilateral triangles. What can you prove about the triangle PQR?
problem

Two and Four Dimensional Numbers

Age

16 to 18

Challenge level

Matrices and Complex Numbers combine to enable us to create four dimensional numbers.
problem

Target Six

Age

16 to 18

Challenge level

Show that x = 1 is a solution of the equation x^(3/2) - 8x^(-3/2) = 7 and find all other solutions.
problem

Cube Roots

Age

16 to 18

Challenge level

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

Thousand Words

Age

16 to 18

Challenge level

Here the diagram says it all. Can you find the diagram?
problem

Sheep in Wolf's Clothing

Age

16 to 18

Challenge level

Can you work out what simple structures have been dressed up in these advanced mathematical representations?
article
An Introduction to Complex Numbers

A short introduction to complex numbers written primarily for students aged 14 to 19.
article
What Are Complex Numbers?

This article introduces complex numbers, brings together into one bigger 'picture' some closely related elementary ideas like vectors and the exponential and trigonometric functions and their derivatives and proves that e^(i pi)= -1.