# Quaternion complex calculus?

1. Sep 11, 2006

### lokofer

"Quaternion complex calculus?"..

Hello my question is if there exist an analogue of "complex calculus" for complex numbers but using "quaternions"..in fact if we define the Quaternion.. $$a+ib+jc+kd$$ with the "commutation relations" $$[x_i ,x_j ]=\epsilon _{ijk} x_k$$ then i would like to know if there exist the equivalent to..

a) "Cauchy-Riemann" equation...( Harmonic functions ?)

b) "cauchy integral formula" (for Surface, Volume or line integrals on this space)

Of course the can be very 2fruitful" specially when studying Relativity since you could consider the Quaternion:

$$Q= cdt-idx-jdy-kdz$$ (x,y,z) space coordinates and t the time.:grumpy: :grumpy:

2. Sep 11, 2006

### MeJennifer

There is a nice website that maintains info and links about quaternions.

Last edited: Sep 11, 2006
3. Sep 11, 2006

### Hurkyl

Staff Emeritus
Much of what's interesting is simply vector analysis in disguise. It would be good to look at that.

Last edited: Sep 11, 2006