Complex Puzzle

Can you use everything you have learned about complex numbers to crack this puzzle?
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative

Problem

This resource is part of our Adventures with Complex Numbers collection



This activity follows on from Into the Wilderness.

Image
Complex Puzzle
 

 

In this diagram, there are several points and the unit circle (the circle with centre at the origin and radius 1).

The points $a$ to $h$ are the sum or product of combinations of $u$, $v$ and $w$.

Can you work out which of the expression below describes each point? 

$u + v$

$u + w$

$v + w$

$u + v + w$

$uv$

$uw$

$vw$

$uvw$


You might now like to start Mapping the Territory.

This problem was inspired by an exercise in Complex Analysis by Ian Stewart and David Tall.