Answer
$\frac{3}{5}-\frac{4}{5}i$
Work Step by Step
Multiply the numerator and denominator by the conjugate of the complex imaginary number.
$\frac{(2-i)}{(2+i)}\times\frac{(2-i)}{(2-i)}$
Use foil to expand numerator; use the difference of two squares to expand the denominator.
$\frac{4-4i+i^2}{4-i^2}$
Remember that $i^2=-1$.
$\frac{4-4i-1}{4+1}$
Combine like terms in both numerator and denominator.
$\frac{3-4i}{5}$
Separate.
$\frac{3}{5}-\frac{4}{5}i$
