  Starting with the braided quantum group $\operatorname{SU}_q(2)$ for a
complex deformation parameter $q$ we perform the construction of the quotient
$\operatorname{SU}_q(2)/\mathbb{T}$ which serves as a model of a quantum
sphere. Then we follow the reasoning of Podle\'{s} who for real $q$ classified
quantum spaces with the action of $\operatorname{SU}_q(2)$ with appropriate
spectral properties. These properties can also be expressed in the context of
the braided quantum $\operatorname{SU}_q(2)$ (with complex $q$) and we find
that they lead to precisely the same family of quantum spaces as found by
Podle\'{s} for the real parameter $|q|$.
