Task B-2.1. Determine the modulus of the complex number $z=\frac{(2+3 i)^{2011}}{(2-3 i)^{2009}}$.
$$
\begin{aligned}
|z| & =\frac{|2+3 i|^{2011}}{|2-3 i|^{2009}}= \\
& =\frac{\sqrt{13}^{2011}}{\sqrt{13}^{2009}}=(\sqrt{13})^{2011-2009}=\sqrt{13}^{2}=13
\end{aligned}
$$

The solution.

$$
\begin{aligned}
|z| & =\frac{|2+3 i|^{2011}}{|2-3 i|^{2009}}= \\
& =\frac{\sqrt{13}^{2011}}{\sqrt{13}^{2009}}=(\sqrt{13})^{2011-2009}=\sqrt{13}^{2}=13
\end{aligned}
$$