Something above complex numbers?

Perhaps you would be interested in quaternions Max (see https://en.wikipedia.org/wiki/Quaternion for example).  These extend the concept of complex numbers.

Can someone answer this please...... My curiousity is telling me to take this knowledge ASAP......

Hi Max,

How about:

$i^i=real\;number$

proof:

$i^i=e^{lni^i}=e^{ilni}\\ \qquad \qquad \text{For complex logs}\\ \qquad \qquad ln(z)=ln|z|+i*arg(z)\\ so\\ ln(i)=ln|i|+i*arg(i)\\ \qquad =ln(1)+i*\frac{\pi}{2}\\ \qquad =i*\frac{\pi}{2}\\~\\ so\\ i^i=e^{lni^i}\\ \:\:\:=e^{i*lni}\\ \:\:\:=e^{i*i*\frac{\pi}{2}}\\ \:\:\:=e^{-1\frac{\pi}{2}}\\ \:\:\:=e^{\frac{-\pi}{2}}\\ $

So maybe we start going in circles    

I had a thought,

Any number divided by itself =1,  even complex numbers.

and

If you multiply a complex number by its conjugate you get a real number too :)