A quaternion is written as: where
a,b,c,d are all real numbers. However, a identifies the real part of the quaterion, while the imaginary part of the quaterion is the combination of i,j and k. These three parts (i,j,k) are orthogonal to each other and satisfy the following relationship:
Another representation of quaternions is amplitude phase representation, which can be expressed as:
where |q| is the amplitude of q, and phi, theta, psi are the phase angle of q
Now, if I would like to get the imaginary parts from this last equation, could I take ? Is it right?