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 a 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 From the given, we have $z_{1}=t+(1-t) \mathrm{i}(0 \leqslant t \leqslant 1) \cdot z_{2}=\cos \theta+\mathrm{i} \sin \theta$, thus
$$
z_{1}+z_{2}=t+\cos \theta+(1-t+\sin \theta) \mathrm{i} \text {. }
$$
$$
(x-t)^{2}+[y-(1-t)]^{2}=1 \text {. }
$$

That is, the point corresponding to $z_{1}+z_{2}$ lies on a circle with center $(t, 1-t)$ and radius equal to 1, and since $(0 \leqslant t \leqslant 1)$. Therefore, the region where the point corresponding to $z_{1}+z_{2}$ is located is the shaded area in the figure.
Its area is
$$
2 \cdot \frac{\pi}{2}+2 \cdot \sqrt{2}=2 \sqrt{2}+\pi \text {. }
$$

Hence, the correct choice is B.