Find the conjugates of the complex numbers [(1 + i) (2 + i)] / (3 + i)

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

Let us convert to standard form,

\( \dfrac{(1 + i) (2 + i)}{(3 + i)}\)

\( =\dfrac{1(2+i)+i(2+i)}{3+i}\)

\( =\dfrac{1+3i}{3+i}\)

\( =\dfrac{1+3i}{3+i}\times \dfrac{3-i}{3-i}\)

\( \dfrac{3}{5}+\dfrac{4i}{5}\)

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

So,

The conjugate of  \( \dfrac{3}{5}+\dfrac{4i}{5}\)