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Câu hỏi: Tìm tất cả các số phức $z$ thỏa mãn $2z-3\left( 1+i \right)=iz+7-3i$.
A. $z=\dfrac{8}{5}-\dfrac{4}{5}i$.
B. $z=4-2i$.
C. $z=\dfrac{8}{5}+\dfrac{4}{5}i$.
D. $z=4+2i$.
A. $z=\dfrac{8}{5}-\dfrac{4}{5}i$.
B. $z=4-2i$.
C. $z=\dfrac{8}{5}+\dfrac{4}{5}i$.
D. $z=4+2i$.
Ta có:
$2z-3\left( 1+i \right)=iz+7-3i\Leftrightarrow 2z-iz=7-3i+3\left( 1+i \right)$
$\Leftrightarrow \left( 2-i \right)z=10\Leftrightarrow z=\dfrac{10}{2-i}\Leftrightarrow z=4+2i$.
$2z-3\left( 1+i \right)=iz+7-3i\Leftrightarrow 2z-iz=7-3i+3\left( 1+i \right)$
$\Leftrightarrow \left( 2-i \right)z=10\Leftrightarrow z=\dfrac{10}{2-i}\Leftrightarrow z=4+2i$.
Đáp án D.