Answer
$\displaystyle \frac{3}{4}-\frac{1}{3}i$
Work Step by Step
$\displaystyle \frac{4+9i}{12i}\qquad$ ...multiply both numerator and denominator by $-i$
$=\displaystyle \frac{4+9i}{12i}\cdot\frac{-i}{-i}$
$=\displaystyle \frac{-i(4+9i)}{-i(12i)}\qquad$ ...use the Distributive property..
$=\displaystyle \frac{(-i)(4)+(-i)(9i)}{-12i^{2}}\qquad$ ...simplify.
$=\displaystyle \frac{-4i-9i^{2}}{-12i^{2}}\qquad$ ...simplify. ($i^{2}=-1$)
$=\displaystyle \frac{9-4i}{12}\qquad$ ...write in standard form
$=\displaystyle \frac{9}{12}-\frac{4i}{12}\qquad$ ...reduce the first fraction with $3$ and the second with $4$.
$=\displaystyle \frac{3}{4}-\frac{1}{3}i$
