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It's known that we can use complex numbers to solve some 2d problems easier than synthetic methods.
But, what do you think about using complex numbers in 3d geometry?

I've found extend of complex numbers - quaternions. Is it possible to solve problems with quaternions ? Is there any book about this method ?

Thanks for help,

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Quaternions are used in computer graphics...there are quite a number of questions on this, some I have answered, but got tired of typing the same thing over and over. The short version is, you write a 3-D point as a pure quaternion $v,$ (zero real part). Then, given a unit quaternion $\xi,$ a rotated pure quaternion comes from $\xi v \bar{\xi}.$ I'm not sure these give much help with contest problems. – Will Jagy Jul 28 '12 at 21:36
I very rarely see 3D problems in Olympiad geometry. Do you have any examples? – Qiaochu Yuan Jul 28 '12 at 22:17
For example this:… – John Smith Jul 28 '12 at 22:54

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