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→Algebraic properties: re square roots |
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From the definition it is apparent that the ring of split-complex numbers is isomorphic to the [[group ring]] {{tmath|\R[C_2]}} of the [[cyclic group]] {{math|C{{sub|2}}}} over the real numbers {{tmath|\R.}}
If a split-complex number has one square root, it has four. Only elements of the [[identity component]] in the [[group of units]] in '''D''' have square roots. Say <math>p = \exp (q), \ \ q \in D. \text{then} \pm \exp(\frac{q}{2}) </math> are square roots of ''p''. Further, <math>\pm j \exp(\frac{q}{2})</math> are also square roots of ''p''.
==Matrix representations==
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