8. Let $a \in \mathbf{R}$, and the complex numbers
$$
z_{1}=a+\mathrm{i}, z_{2}=2 a+2 \mathrm{i}, z_{3}=3 a+4 \mathrm{i} \text {. }
$$

If $\left|z_{1}\right|, \left|z_{2}\right|, \left|z_{3}\right|$ form a geometric sequence, then the value of the real number $a$ is . $\qquad$
8. 0 .

From the condition, we know that $\left|z_{1}\right|\left|z_{3}\right|=\left|z_{2}\right|^{2}$.
Notice that, $\left|z_{2}\right|=2\left|z_{1}\right|$.
Then $\left|z_{3}\right|=4\left|z_{1}\right|$
$$
\begin{array}{l}
\Rightarrow \sqrt{9 a^{2}+16}=4 \sqrt{a^{2}+1} \\
\Rightarrow a=0 .
\end{array}
$$