Sets of exact approximation order by complex rational numbers

For a nonincreasing function $\psi$, let $\textrm{Exact}(\psi)$ be the set of complex numbers that are approximable by rational to order $\psi$ but no better order. In this paper, we obtain Hausdorff dimension and packing when $\psi(x)=o(x^{-2})$. We also prove lower bound is greater than $2-\tau/(1-2\tau)$ $\tau=\limsup_{x\to\infty}\psi(x)x^2$ small enough.