2. Let the complex number $z$ satisfy $(z-\mathrm{i})(\bar{z}+\mathrm{i}) \leqslant 1$. Then, the set of points corresponding to $z$ in the complex plane forms the figure ( ).
(A) a circle with center at $(1,0)$ and radius 1, and its interior
(B) a circle with center at $(0,1)$ and radius 1, and its interior
(C) a circle with center at $(-1,0)$ and radius 1, and its interior
(D) a circle with center at $(0,-1)$ and radius 1, and its interior
2.B.

Let $z=a+b \mathrm{i}$, then we have
$$
\begin{array}{l}
(z-\mathrm{i})(\bar{z}+\mathrm{i})=(a+b \mathrm{i}-\mathrm{i})[a-(b \mathrm{i}-\mathrm{i})] \\
=a^{2}+(b-1)^{2} \leqslant 1 .
\end{array}
$$

Therefore, its graph is a circle with center at $(0,1)$ and radius 1, including the interior of the circle.