### Roots and Coefficients

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?

### Three by One

There are many different methods to solve this geometrical problem - how many can you find?

### Complex Rotations

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?

# Target Six

##### Age 16 to 18 Challenge Level:

Show that $x = 1$ is a solution of the equation

$$x^{3/2} - 8x^{-3/2} = 7$$

Find all the solutions of the equation.