\({\rm{w}} = x + yi \Rightarrow x + yi = 3 - 2i + \left( {2 - i} \right)z \Leftrightarrow \frac{{x + yi - 3 + 2i}}{{2 - i}} = z\)

\( \Rightarrow \frac{{2x + 2yi - 6 + 4i + xi - y - 3i - 2}}{5} = z \Leftrightarrow \frac{{i\left( {x + 2y + 1} \right) + 2x - y - 8}}{5} = z\)

\( \Rightarrow {\left( {x + 2y + 1} \right)^2} + {\left( {2x - y - 8} \right)^2} = 25.9 = 5{x^2} + 5{y^2} - 30x + 20y + 65\)

\(\begin{array}{l} \Leftrightarrow 5.9 = {x^2} + {y^2} - 6x + 4y + 13 = {\left( {x - 3} \right)^2} + {\left( {y - 2} \right)^2}\\ \Rightarrow R = 3\sqrt 5 .\end{array}\)