Answer
$\frac{9+83i}{85}$
Work Step by Step
Using the rules of imaginary numbers:
$\frac{1}{2+i} = \frac{2-i}{2-i}=\frac{2-i}{2^2-i^2}=\frac{2-i}{5}$
$\frac{5}{1+4i} = \frac{5}{1+4i}*\frac{1-4i}{1-4i}=\frac{5-20i}{1-16i^2}=\frac{5-20i}{17}$
Write the final expression:
$\frac{2-i}{5}-\frac{5-20i}{17} = \frac{17(2-i)+5(5-20i)}{17*5} = $$\frac{9+83i}{85}$
