Answer
$=\displaystyle \frac{2}{13}+\frac{29}{13}i$
Work Step by Step
$\displaystyle \frac{7+4i}{2-3i}\qquad$ ...multiply both numerator and denominator by $2+3i$
$=\displaystyle \frac{(7+4i)(2+3i)}{(2-3i)(2+3i)}\qquad$ ...use the FOIL method.
$=\displaystyle \frac{7\cdot 2+7\cdot 3i+4i\cdot 2+4i\cdot 3i}{2\cdot 2+2\cdot 3i+(-3i)\cdot 2+(-3i)(3i)}\qquad$ ...simplify.
$=\displaystyle \frac{14+21i+8i+12i^{2}}{4+6i-6i-9i^{2}}\qquad$ ...simplify. ($i^{2}=-1$)
$=\displaystyle \frac{14+29i-12}{4+9}\qquad$ ...add like terms.
$=\displaystyle \frac{2+29i}{13}\qquad$ ...write in standard form
$=\displaystyle \frac{2}{13}+\frac{29}{13}i$
