Question

O conjugado de 2 - i/2 + i vale ?

Answer 1

$\dfrac{2-i}{2+i}$

Multiplicando o numerador e o denominador pelo conjugado do denominador:

$\dfrac{2-i}{2+i}=\dfrac{(2-i)(2-i)}{(2+i)(2-i)}\\\\\\\dfrac{2-i}{2+i}=\dfrac{(2-i)^{2}}{2^{2}-i^{2}}\\\\\\\dfrac{2-i}{2+i}=\dfrac{2^{2}-2\cdot2\cdot i+i^{2}}{4-(-1)}\\\\\\\dfrac{2-i}{2+i}=\dfrac{4-4i-1}{4+1}\\\\\\\dfrac{2-i}{2+i}=\dfrac{3-4i}{5}\\\\\\\boxed{\boxed{\dfrac{2-i}{2+i}=\dfrac{3}{5}-\dfrac{4}{5}i}}$

Seja z esse número. O conjugado dele será dado por:

$\boxed{\boxed{\overline{z}=\dfrac{3}{5}+\dfrac{4}{5}i}}$