8. In the complex plane, the point corresponding to the complex number $z_{1}$ moves on the line segment connecting 1 and $\mathrm{i}$, and the point corresponding to the complex number $z_{2}$ moves on the circle centered at the origin with a radius of 1. Then the area of the region where the point corresponding to the complex number $z_{1}+z_{2}$ is located is ( ).
(A) $4+\pi$
(B) $2 \sqrt{2}+\pi$
(C) $\pi$
(D) $\frac{3 \pi}{2}+1$
8. B.

From the given, $z_{1}=t+(1-t) \mathrm{i}(0 \leqslant t \leqslant 1)$.
From $z_{2}=\cos \theta+\mathrm{i} \sin \theta$, we get $z_{1}+z_{2}=t+\cos \theta+(1-t+\sin \theta) \mathrm{i}$.
Let $z_{1}+z_{2}=x+y \mathrm{i}$. Then $\left\{\begin{array}{l}x=t+\cos \theta, \\ y=1-t+\sin \theta \text {. }\end{array}\right.$
Eliminating $\theta$ yields $(x-t)^{2}+[y-(1-t)]^{2}=1$.
Thus, the point corresponding to $z_{1}+z_{2}$ lies on a circle with center $(t, 1-t)$ $(0 \leqslant t \leqslant 1)$ and radius 1.

Therefore, the region where the point corresponding to $z_{1}+z_{2}$ lies is the shaded part in Figure 2. Its area is
$$
\begin{array}{l}
2 \cdot \frac{\pi}{2}+2 \sqrt{2} \\
=2 \sqrt{2}+\pi .
\end{array}
$$