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Hey guys so I was thinking about how to extend the Complex Plane out to a third dimension and I started reading the whole tidbit about Quaternions and their mechanics when I realized that I want to propose a whole new question. Now please feel free to prove me wrong if you can answer it because I haven't found a whole lot.

Imagine a number J who satisfies the solution to the following equation

Log

FOR ALL B:

There is no complex number that satisfies that solution and I believe (as uneducated as I might be in this subject) that there is no Quaternion, Octonion or any type of standard Algebraic extension of the number line that satisfies this equation. If this number J can be proposed as the new number extension to the complex plane, then,

We get numbers being described in the form of:

a + bi + cj. Now keeping in mind the ability for numbers to cross:

a + bi + cj + dji is what this number can look like...

What's your take on it?

Imagine a number J who satisfies the solution to the following equation

Log

_{b}(J) = -bFOR ALL B:

There is no complex number that satisfies that solution and I believe (as uneducated as I might be in this subject) that there is no Quaternion, Octonion or any type of standard Algebraic extension of the number line that satisfies this equation. If this number J can be proposed as the new number extension to the complex plane, then,

We get numbers being described in the form of:

a + bi + cj. Now keeping in mind the ability for numbers to cross:

a + bi + cj + dji is what this number can look like...

What's your take on it?

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