As others have noted, we don't have 3D numbers because there is a theorem saying that they don't exist (at least with norm). Interestingly, Hamilton's discovery of the quaternions was the result of a long and fruitless search for a three-dimensional analog to the complex numbers.
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As others have noted, we don't have 3D numbers because there is a theorem saying that they don't exist (at least with norm). Interestingly, Hamilton's discovery of the quaternions was the result of a long and fruitless search for a three-dimensional analog to the complex numbers.