  In this work we study the Plancherel-Rotach type asymptotics for selected
$q$-series and $q$-orthogonal polynomials with complex scalings. The $q$-series
we cover are Euler's $q$-exponential, Ramanujan function, Jackson's $q$-Bessel
function of second kind, Ismail-Masson orthogonal polynomials, Stieltjes-Wigert
polynomials and $q$-Laguerre polynomials. For a fixed $q$ with $0<q<1$, in each
case the main term of the asymptotic formulas may contain Ramanujan function or
theta function depending on the value of scaling parameter. Furthemore, when
the scaling parameter is in certain strip of the complex plane, its number
theoretical property completely determines the order of the error term. In each
cases, we also investigate the asymptotic behavior of the mentioned $q$-series
when $q$ approaching 1 in a restricted manner. These asymptotic formulas may
provide insights to new random matrix models.
