Solution
= Solution
Multiply by the <complex conjugate> of the denominator:
$$
\frac{2+3i}{4-5i}=\frac{(2+3i)(4+5i)}{4^2+5^2}
=\frac{-7+22i}{41}.
$$
Thus the <real part> and <imaginary part> are respectively
$$
\boxed{-\frac7{41},\qquad\frac{22}{41}}.
$$