If you have never met complex numbers before, these problems offer a gentle introduction before challenging you to use different representations to visualise what happens when complex numbers are manipulated in different ways.
problem
A brief introduction to complex numbers
Age
14 to 18
Challenge level
In this problem, we define complex numbers and invite you to explore what happens when you add and multiply them.
problem
A brief introduction to the Argand diagram
Age
14 to 18
Challenge level
Complex numbers can be represented graphically using an Argand diagram. This problem explains more...
problem
Complex squares
Age
16 to 18
Challenge level
What happens when we square complex numbers? Can the square of a complex number be real?
list
The Twizzle Trail
Age
14 to 16
Challenge level
A geometrical arithmetic that can lead to complex numbers