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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.