When Gauss discovered Complex Numbers he found he could use them to factorise
Primes. For instance 2 can be factorised as (1+i)*(1-i). Only half the Primes
can be factorised like this, but there are Hypercomplex Numbers, like
Quaternions, which can be used to carry the process further.
Recently this topic seems to have attracted further research, and it seems to
me this could be connected with Cryptography and its use of enormous Primes.
Apparently the People's Republic of China are getting expert at cracking
apparently uncrackable ciphers. Does anybody know more about this?
Faictz Ce Que Vouldras: Frank Mitchell
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I'm surprised at you fellas:
The whole point is that "i" or "j" is the Square Root of Minus One.
Thus minus i squared equals Plus One. So:
(2+i)*(2-i) = 4+1 = 5
(3+2i)*(3-2i) = 9+4 =13
Quaternions have 3 different square roots of -1, called i, j, k, and they too
have Complex Conjugates like Complex Numbers. The Imaginary Components i, j, k
then gave us the idea of Vectors. Divide two Vectors and you get a Quaternion.
Faictz Ce Que Vouldras: Frank Mitchell