$HS\left(-Im(Y)\left(Re(A)\left(Re(S)Im(\alpha )+Re(\alpha )Im(S)\right)+Im(A)\left(Re(S)Re(\alpha )-Im(S)Im(\alpha )\right)\right)+Re(Y)\left(-Im(A)\left(Re(S)Im(\alpha )+Re(\alpha )Im(S)\right)+Re(A)\left(Re(S)Re(\alpha )-Im(S)Im(\alpha )\right)\right)\right)$