Question

O quociente $\frac{8+i}{2-i}$é igual a:

Answer 1

Olá só multiplicar o numerador e o denominador pelo conjugado do denominador (conjugado é a inversão do sinal da parte imaginária do complexo)

e lembre-se, i² = -1

$\dfrac{8+i}{2-i}= \dfrac{(8+i)\cdot(2+i)}{(2-i)\cdot(2+i)} \\\\\\ \dfrac{8+i}{2-i}= \dfrac{16+8i+2i+i^2}{4-i^2}\\\\\\ \dfrac{8+i}{2-i}= \dfrac{16+10i+(-1)}{4-(-1)}\\\\\\ \dfrac{8+i}{2-i}= \dfrac{16-1+10i}{4+1}\\\\\\ \dfrac{8+i}{2-i}= \dfrac{15+10i}{5}\\\\\\ \dfrac{8+i}{2-i}= \dfrac{15}{5}+ \dfrac{10i}{5}\\\\\\ \Large\boxed{\dfrac{8+i}{2-i}=3+2i}$