Complex numbers

problem
Cube roots

Age

16 to 18

Challenge level

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

Age

16 to 18

Challenge level

Choose some complex numbers and mark them by points on a graph. Multiply your numbers by i once, twice, three times, four times, ..., n times? What happens?
problem
8 methods for three by one

Age

14 to 18

Challenge level

This problem in geometry has been solved in no less than EIGHT ways by a pair of students. How would you solve it? How many of their solutions can you follow? How are they the same or different? Which do you like best?
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
Roots and coefficients

Age

16 to 18

Challenge level

If xyz = 1 and x+y+z =1/x + 1/y + 1/z show that at least one of these numbers must be 1. Now for the complexity! When are the other numbers real and when are they complex?
article
What are numbers?

Ranging from kindergarten mathematics to the fringe of research this informal article paints the big picture of number in a non technical way suitable for primary teachers and older students.
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.
article
An introduction to complex numbers

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

Age

14 to 18

Challenge level

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