Find the conjugates of the complex numbers 1/(3 + 5i)

Given:

\( \dfrac{1}{(3 + 5i)}\)

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

Let us convert to standard form by multiplying and dividing with (3 – 5i)

We get,

\( \dfrac{1}{(3 + 5i)}\times \dfrac{3-5i}{(3 - 5i)}\)

\( =\dfrac{3-5i}{34}\)

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

So,

The conjugate of \( =\dfrac{3-5i}{34}\) is \( =\dfrac{3+5i}{34}\)