Answer
$\dfrac{11}{61}+\dfrac{60i}{61}$
Work Step by Step
Multiplying by the conjugate of the denominator, the expression $
\dfrac{6+5i}{6-5i}
$ simplifies to
\begin{array}{l}
\dfrac{6+5i}{6-5i}
\cdot
\dfrac{6+5i}{6+5i}
\\\\=
\dfrac{6(6)+6(5i)+5i(6)+5i(5i)}{(6)^2-(5i)^2}
\\\\=
\dfrac{36+30i+30i+25i^2}{36-25i^2}
\\\\=
\dfrac{36+60i+25(-1)}{36-25(-1)}
\\\\=
\dfrac{11+60i}{61}
\\\\=
\dfrac{11}{61}+\dfrac{60i}{61}
.\end{array}
