Subject: Algebraic equations in quaternions
Date: Tue, 03 Mar 1998 06:00:38 PST
From: David

Hello! My name is David, and I live in Sweden. First of all i whish to apologize for my imperfect english. I am a Math-freak you see, and I really want to thank you for this splendid site of yours containing information on such things I never thought anyone would bother to write about on the net. Thank You!

A second reason for me to email you is that I do have a question of mathematical character.I'd be undescribable happy if you would bother to answer little me.

This is the question: I've newly confrontet the Hypercomplex numbers. So now I know that Hamilton gives the equation x2+1=0 as many as 6 solutions, +/- i,j and k, and that multiplication is not neccessserally (My god, How do I spell that?) comucative (Is that the english word? What Im reffering to is the phenomenom of u*v might not equal v*u)

Gauss proofed that an polynomialequation of degree n have at least one and at maximum n different roots in the complex plane. Now I wonder, how many roots might a p.equation of degree n have in the hypercomplex plane? The equation x2+1=0 has then not 2 solutions but 6! Would a p-equation for example have as maximum 3n (or in some other relation to n) number of solutions instead of n as in the "ordinary" math? Could You please bring light to mig bothered head in this matter?

I really hope you can tell me what you now about how the greatest possible number of solutions to a P.eq. in the hypercomplex numberspace depends on its degree n.

If so, you will find my email at

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