Question

Find the conjugate of the following complex number:

\[\frac{(3 - i )^2}{2 + i}\]

Answer 1

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

\[ = \frac{\left( 9 - 6i - 1 \right)}{2 + i}\]

\[ = \frac{8 - 6i}{2 + i} \times \frac{2 - i}{2 - i}\]

\[ = \frac{16 - 8i - 12i + 6 i^2}{4 - i^2}\]

\[ = \frac{10 - 20i}{5}\]

\[ = 2 - 4i\]

\[ \therefore z = 2 + 4i\]