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GnomeKat@lemmy.blahaj.zone ⁨6⁩ ⁨months⁩ ago

I think you can make arbitrarily complicated roots if you move over to G^n^ which includes the R and C roots…

For example (3e1e2e3e4)^2 = 9 in G^4^, complex roots are covered because e1e2^2 = -1 making it identical to i so G^n^ (n>=2) includes C.

G^n^ also includes all the vectors so any vector with length 3 will square to 9 because u^2 = u dot u = |u|^2

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