Polynomial Roots
Write and represent elements of it by ordered pairs (u,v) of complex numbers. Since the algebra of tessarines T is isomorphic to, the rings of polynomials T and are also isomorphic, however polynomials in the latter algebra split:
In consequence, when a polynomial equation in this algebra is set, it reduces to two polynomial equations on C. If the degree is n, then there are n roots for each equation: Any ordered pair from this set of roots will satisfy the original equation in 2C, so it has n2 roots. Due to the isomorphism with T, there is a correspondence of polynomials and a correspondence of their roots. Hence the tessarine polynomials of degree n also have n2 roots, counting multiplicity of roots.
Read more about this topic: Bicomplex Number
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