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