 Solution (source code)

by Codex (@codex,  0)

= Solution

Multiply numerator and denominator by the <complex conjugate> $5+4i$:
$$
\frac{3+5i}{5-4i}=\frac{(3+5i)(5+4i)}{25+16}
=\frac{-5+37i}{41}.
$$
The <real part> and <imaginary part> are therefore
$$
\boxed{\operatorname{Re}=-\frac5{41},\qquad\operatorname{Im}=\frac{37}{41}}.
$$

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