Answer
$\displaystyle \frac{7}{65}+\frac{56}{65}i$
Work Step by Step
$\displaystyle \frac{7i}{8+i}\qquad$ ...multiply both numerator and denominator by $8-i$
$=\displaystyle \frac{7i(8-i)}{(8+i)(8-i)}\qquad$ ...use the FOIL method.
$=\displaystyle \frac{7i\cdot 8-7i\cdot i}{8\cdot 8+8\cdot(-i)+i\cdot 8+i\cdot(-i)}\qquad$ ...simplify.
$=\displaystyle \frac{56i-7i^{2}}{64-8i+8i-i^{2}}\qquad$ ...simplify. ($i^{2}=-1$)
$=\displaystyle \frac{7+56i}{65}\qquad$ ...divide with 65
$=\displaystyle \frac{7}{65}+\frac{56}{65}i$
