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Câu hỏi: Số phức z thỏa mãn $z\left( 2-i \right)+13i=1$ có môđun là
A. $\left| z \right|=\sqrt{34}$
B. $\left| z \right|=34$
C. $\left| z \right|=\dfrac{5\sqrt{34}}{3}$
D. $\left| z \right|=\dfrac{\sqrt{34}}{3}$
A. $\left| z \right|=\sqrt{34}$
B. $\left| z \right|=34$
C. $\left| z \right|=\dfrac{5\sqrt{34}}{3}$
D. $\left| z \right|=\dfrac{\sqrt{34}}{3}$
$z\left( 2-i \right)+13i=1\Leftrightarrow z=\dfrac{1-13i}{2-i}\Leftrightarrow z=\dfrac{\left( 1-13i \right)\left( 2+i \right)}{\left( 2-i \right)\left( 2+i \right)}\Leftrightarrow z=3-5i$
$\left| z \right|=\sqrt{{{3}^{2}}+{{\left( -5 \right)}^{2}}}=\sqrt{34}$
$\left| z \right|=\sqrt{{{3}^{2}}+{{\left( -5 \right)}^{2}}}=\sqrt{34}$
Đáp án A.