When you rewrite the angular momentum generators Ji and boost generators Kj in terms of the linear combinations N±i=Ji±iKi, does this mean that your group parameters can now be complex? So for example a group element R can be written as: [tex]R(z_1,z_2)=\exp[i(z_1 N^+ +z_2 N^-)] [/tex] where the z's are complex? z1 and z2 must be complex conjugates in order to get something of the form: [tex]R(z_1,z_2)=R(x,y)=\exp[i(xJ+yK)] [/tex] where x and y are real group parameters instead of complex ones. So is there an implicit rule that whatever the coefficient of N+, the coefficient of N- must be the complex conjugate? So in order to specify a group element of SO(4), you have to give 3 complex numbers (one for i=1,2,3), and the coefficients in front of the N- generators would just be the complex conjugate of those numbers?