Complex numbers

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.
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.
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?
problem
Sextet

Age

16 to 18

Challenge level

Investigate x to the power n plus 1 over x to the power n when x plus 1 over x equals 1.
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
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
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?
$Complex partial fractions$

problem
Complex partial fractions

Age

16 to 18

Challenge level

To break down an algebraic fraction into partial fractions in which all the denominators are linear and all the numerators are constants you sometimes need complex numbers.
problem
Footprints

Age

16 to 18

Challenge level

Make a footprint pattern using only reflections.