Answer
$-\dfrac{5}{2}-4i$
Work Step by Step
Multiply both the numerator and the denominator by the conjugate of the denominator, which is $-2i$, to obtain:
$=\dfrac{(8-5i)(-2i)}{2i(-2i)}
\\=\dfrac{-16i+10i^2}{-4i^2}$
Use the fact that $i^2=-1$ to obtain:
$=\dfrac{-16i+10(-1)}{-4(-1)}
\\=\dfrac{-16i-10}{4}
\\=-\dfrac{-10-16i}{4}
\\=-\dfrac{10}{4} - \dfrac{16}{4}i
\\=-\dfrac{5}{2}-4i$
