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# Complex Puzzle

*This activity follows on from Into the Wilderness.*

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?

*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.*

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Age 14 to 18

Challenge Level

*This resource is part of our Adventures with Complex Numbers collection*

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?

$u + v$

$u + w$

$v + w$

$u + v + w$

$uv$

$uw$

$vw$

$uvw$

$u + w$

$v + w$

$u + v + w$

$uv$

$uw$

$vw$

$uvw$