Confuted/Blackrat: quaternion question

this is aimed towards confuted/blackrat, I saw jdinger do the same thing aimed towards me (but others answered) so this is aimed at confuted but anyone can answer.

Anyway before I got so friggin sick I read finding the quaternion itself is actually extremely simple, that it is just:

q = cos(theta/2) + A sin(theta/2)

of course they had to go through a ton of confusing theory and complex equations first, and then they just used identities to break it down

A is the unit axis you are rotating about

However I have no clue how to apply this. It says I have to use the 'homomorphism'

q P q-1

to perform the rotation, where P stands for the point/vector you are rotating. However, I'm not entirely sure what I'm doing!!! Is q-1 the inverse of the quaternion or the conjugate of the quaternion? In my math book they seem to use q-1 as the conjugate, when it *should* mean the inverse. and my understanding is that the inverse is:

conjugate over modulus squared

the modulus of a complex number is z is:

z * conjugateofz

and the conjugate is where the imaginary part is negated, and using the definition i = sqrt(-1) you get:

z * conjugate = (a + bi) ( a - bi) = a^2 + b^2

anyway back to quaternions, if you can just explain what I'm doing here with :

q P q-1 and how to actually carry out that multiplication I'd be happy!