Answer:
A
Step-by-step explanation:
Given
[tex]\frac{2-i}{2+i}[/tex]
Multiply the numerator/ denominator by the conjugate of the denominator.
The conjugate of 2 + i is 2 - i , then
= [tex]\frac{(2-i)(2-i)}{(2+i)(2-i)}[/tex] ← expand numerator/ denominator using FOIL
= [tex]\frac{4-4i+i^2}{4-i^2}[/tex] [ i = [tex]\sqrt{-1}[/tex] ⇒ i² = - 1 ]
= [tex]\frac{4-4i-1}{4+1}[/tex]
= [tex]\frac{3-4i}{5}[/tex]
= [tex]\frac{3}{5}[/tex] - [tex]\frac{4}{5}[/tex] i → A
