Answer
$\dfrac{18}{25}+\dfrac{26}{25}i$
Work Step by Step
Multiplying by the conjugate of the denominator of $
\dfrac{6+2i}{4-3i}
$ results to
\begin{array}{l}
\dfrac{6+2i}{4-3i}
\cdot
\dfrac{4+3i}{4+3i}
\\\\=
\dfrac{6(4)+6(3i)+2i(4)+2i(3i)}{(4)^2-(3i)^2}
\\\\=
\dfrac{24+18i+8i+6i^2}{16-9i^2}
\\\\=
\dfrac{24+18i+8i+6(-1)}{16-9(-1)}
\\\\=
\dfrac{18+26i}{25}
\\\\=
\dfrac{18}{25}+\dfrac{26}{25}i
.\end{array}
