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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?

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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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8 Methods for Three by One

This problem in geometry has been solved in no less than EIGHT ways by a pair of students. How would you solve it? How many of their solutions can you follow? How are they the same or different? Which do you like best?

Complex Countdown

Age 16 to 18 Challenge Level:
Here are a couple of games of complex countdown in action to give you some ideas of how to get started. We use square brackets [ ... ] to show that we are using up one of the original cards.


One possible solution here is
[8+9i] + [-2 - 9i]  + [0-7i]  + ([8i]/[4-0i])


One possible solution is [-1 - 4i] - [-8i]/([8]/[-2])



Arg[-4i] - (Re[7+1i] x Im[-8i]) + [-1]