## Algebra 2 (1st Edition)

$\displaystyle \frac{3}{4}-\frac{1}{3}i$
$\displaystyle \frac{4+9i}{12i}\qquad$ ...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 $4$. $=\displaystyle \frac{3}{4}-\frac{1}{3}i$