Answer 1

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

\[ = \frac{6 + 9i - 4i - 6 i^2}{2 - i + 4i - 2 i^2}\]

\[ = \frac{6 + 6 + 5i}{2 + 2 + 3i}\]

\[ = \frac{12 + 5i}{4 + 3i} \times \frac{4 - 3i}{4 - 3i}\]

\[ = \frac{48 - 36i + 20i - 15 i^2}{16 - 9 i^2}\]

\[ = \frac{63 - 16i}{25}\]

 `therefore overlineZ =(63 +16i)/25`