What is the square root of complex number i? Square root of number -1 defined as i, then what is the square root of complex number i?, I would say it should be j as logic suggests but it's not defined in quaternion theory in that way, am I wrong?
EDIT: my question is rather related to nomenclature of definition, while square root of -1 defined as i, why not j defined as square root of i and k square root of j and  if those numbers have deeper meanings and usage as in quaternions theory.

I think this would be easier to see by writing $i$ in its polar form,
$$i=e^{i\pi/2}$$ 
This shows us that one square root of $i$ is given by 
$$i^{1/2}=e^{i\pi/4} $$
