Find the conjugates of the complex numbers (3 – i)2 /(2 + i)

Since the given complex number is not in the standard form of (a + ib)

Let us convert to standard form,

\( \dfrac{(3-i)^2}{2+i}=\dfrac{3^2+i^2-2(3)(i)}{2+i}\)

\( =\dfrac{8-6i}{2+i}\)

\( \dfrac{8-6i}{2+i}\times \dfrac{2-i}{2-i}\)

\( \dfrac{8(2-i)-6i(2-i)}{2^2-i^2}\)

= 2 - 4i

We know the conjugate of a complex number (a + ib) is (a – ib)

So,

The conjugate of (2 – 4i) is (2 + 4i)