Simplify $\dfrac{5+12i}{2-8i}$. Your answer should be of the form $a+bi$, where $a$ and $b$ are both real numbers and written as improper fractions (if necessary).
\($\dfrac{5+12i}{2-8i}$\)
Multiply numerator / denominator by 2 + 8i
( 5 + 12i) ( 2 + 8i) 10 + 24i + 40i + 96i^2 10 + 64i - 96 -86 + 64i
______________ = ____________________ = ___________ = ________ =
(2 - 8i) (2 + 8i) 4 - 64i^2 68 68
-43 + 32i
_______
34
