1999-10-07|Sunatori's MultiDimensional HyperComplex Number

Here is what my Mathematical Handbook says:
- A complex number is generally written as (a + bi) where "a" and "b" are real numbers and "i", called the imaginary unit, has the property that i^2 = -1.
Now, I liberate myself from the rigid box of the educational system and the establishment in order to use an open inventor mindset and a free spirit. Here are a couple of questions:
- Because y = x^1.5 is equivalent to y^2 = x^3, if x = -1 then y = i. Hence, y = x^1.5 cannot be plotted for x < 0. What about other fractions such as y = x^1.000001 and y = x^1.999999? My Graphing Calculator does not plot these for x < 0. Maybe arbitrary definitions of (-1)^2 = 1 and i^2 = -1 ended up hiding other dimensions.
- Could we define a hypercomplex number to be written as (a + bi + cj) where "a", "b" and "c" are real numbers, "i" (imaginary number) has the property that i^2 = -1, and "j" (jmaginary number) has the property that j^3 = -1? Then, could the series continue infinitely, i.e., "i", "j", "k", "l", "m", ...?
My mathematician (M.Sc.) wife does not have the answer, so I solicit enlightenment by a plurality of Mensa members on the InventNet Forum. The multidimensional hypercomplex number may result in the multi-dimensional Schrödinger Wave Equation and the discovery of Parallel Universe, let alone millions of new inventions!?

Sunatori, Go Simon
- Personal Profile
  - Opinions
    - 1999-10-07|Sunatori's MultiDimensional HyperComplex Number [You are here!]