Answer 1

\[1/\sqrt{26}\]

\[\text { Let  }z = \frac{1}{\left( 1 - i \right)\left( 2 + 3i \right)}\]

\[ \Rightarrow z = \frac{1}{2 + i - 3 i^2} \]

\[ \Rightarrow z = \frac{1}{2 + i + 3}\]

\[\Rightarrow z=\frac{1}{5 + i}\times\frac{5 - i}{5 - i}\]

\[\Rightarrow z=\frac{5 - i}{25 - i^2}\]

\[ \Rightarrow z=\frac{5 - i}{25 + 1}\]

\[\Rightarrow z=\frac{5 - i}{26}\]

\[\Rightarrow z = \frac{5}{26} - \frac{i}{26}\]

\[\Rightarrow \left| z \right|=\sqrt{\frac{25}{676} + \frac{1}{676}}\]

\[\Rightarrow z = \frac{1}{\sqrt{26}}\]