I'm trying to understand hypercomplex numbers by extrapolating from 3blue1brown's explanation of regular complex numbers but it's not working.

It seems like it should just be equal to k because the number line would just be rotated into each plane sequentially. Am I understanding it wrong, or does 3blue1brown's explanation only apply to the ordinary complex numbers?

ALSO, on an unrelated complex number issue, would a transfinite imaginary or complex number necessarily be a special kind of transfinite number? It seems to me that complex numbers don;t meet the definition of either cardinal or ordinal