Answer
$\frac{23}{25}+\frac{14}{25}i$, or (I)
Work Step by Step
For these kind of problems, multiply both the top and bottom by the conjugate of the denominator:
$denom = 4+3i, \ conjugate = 4-3i$
FOIL (multiply out) both the top and the bottom, keeping in mind that $i^2 = -1$
$\frac{2+5i}{4+3i}*\frac{4-3i}{4-3i} = \frac{8-6i+20i-15i^2}{16-9i^2} = \frac{23+14i}{25} = \frac{23}{25}+\frac{14}{25}i$
