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## 'Roots and Coefficients' printed from http://nrich.maths.org/

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?