2. Let the complex number $z$ satisfy $z+9=10 \bar{z}+22 \mathrm{i}$, then the value of $|z|$ is $\qquad$
$$
\begin{array}{l}
\text { Let } z=a+b \mathrm{i}(a, b \in \mathbf{R}) \text {, then } z+9=10 \bar{z}+22 \mathrm{i} \Rightarrow a+9+b \mathrm{i}=10 a+(22-10 b) \mathrm{i} \\
\Rightarrow\left\{\begin{array} { l } 
{ a + 9 = 1 0 a , } \\
{ b = 2 2 - 1 0 b }
\end{array} \Rightarrow \left\{\begin{array}{l}
a=1, \\
b=2
\end{array} \Rightarrow z=1+2 \mathrm{i}|z|=\sqrt{5}\right.\right. \text {. }
\end{array}
$$