Answer
$\dfrac{2-i}{2+i}=\dfrac{3}{5}-\dfrac{4}{5}i$
Work Step by Step
$\dfrac{2-i}{2+i}$
Begin the evaluation of the quotient by multiplying the numerator and the denominator by the complex conjugate of the denominator:
$\dfrac{2-i}{2+i}\cdot\dfrac{2-i}{2-i}=\dfrac{(2-i)^{2}}{2^{2}-i^{2}}=...$
Evaluate the operations indicated in the numerator and in the denominator:
$...=\dfrac{4-(2)(2)i+i^{2}}{4-i^{2}}=\dfrac{4-4i+i^{2}}{4-i^{2}}=...$
Substitute $i^{2}$ by $-1$ and simplify:
$...=\dfrac{4-4i-1}{4-(-1)}=\dfrac{3-4i}{4+1}=\dfrac{3-4i}{5}=\dfrac{3}{5}-\dfrac{4}{5}i$
