Answer
$-\displaystyle \frac{5}{3}+\frac{2}{3}i$
Work Step by Step
$\displaystyle \frac{-2-5i}{3i}\qquad$ ...multiply both numerator and denominator by $-i$
$\displaystyle \frac{(-2-5i)(-i)}{3i(-i)}\qquad$ ...use the FOIL method.
$=\displaystyle \frac{(-2)(-i)+(-5i)(-i)}{-3i^{2}}\qquad$ ...simplify.
$=\displaystyle \frac{2i+5i^{2}}{-3i^{2}}\qquad$ ...simplify. ($i^{2}=-1$)
$=\displaystyle \frac{2i-5}{3}\qquad$ ...write in standard form
$=-\displaystyle \frac{5}{3}+\frac{2}{3}i$
