8. Let $a \in \mathbf{R}$, complex numbers $z_{1}=a+\mathrm{i}, z_{2}=2 a+2 \mathrm{i}, z_{3}=3 a+4 \mathrm{i}$, where $\mathrm{i}$ is the imaginary unit. 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 $\qquad$.
$$
4\left(a^{2}+1\right)=\sqrt{a^{2}+1} \cdot \sqrt{9 a^{2}+16} \Rightarrow 9 a^{2}+16=16\left(a^{2}+1\right) \Rightarrow a=0
$$