Tìm số phức z thỏa mãn (2+i)z - i + 3 = 1 + 3i/2 - i A. -8/5 + 11/5i; B. -4/5 + 8/5i;

Đáp án đúng là: B

$\left(2+i\right)z-i+3=\frac{1+3i}{2-i}$

$\iff \left(2+i\right)z-i+3=\frac{\left(1+3i\right).\left(2+i\right)}{\left(2-i\right).\left(2+i\right)}$

$\iff \left(2+i\right)z-i+3=\frac{-1+7i}{5}$

$\iff \left(2+i\right)z=\frac{-16+12i}{5}$

$\iff z=\frac{4-8i}{5\left(2+i\right)}=\frac{\left(-16+12i\right).\left(2-i\right)}{5\left(2+i\right).\left(2-i\right)}$

$=\frac{40i-20}{25}=-\frac{4}{5}+\frac{8}{5}i.$