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Three by One

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

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Target Six

Show that x = 1 is a solution of the equation x^(3/2) - 8x^(-3/2) = 7 and find all other solutions.

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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?

Roots and Coefficients

Age 16 to 18 Challenge Level:

If \[z_1 z_2 z_3 = 1\] and \[z_1 + z_2 + z_3 = \frac{1}{z_1} + \frac{1}{z_2} +\frac{1}{z_3}\] then 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?