Question

Find the conjugate of the following complex number:

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

Answer 1

$$\text{ Let }z=\frac{{(3-i)}^2}{2+i}$$

$$=\frac{(9-6i-1)}{2+i}$$

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

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

$$=\frac{10-20i}{5}$$

$$=2-4i$$

$$\therefore z=2+4i$$