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Câu hỏi: Cho hai số phức ${{z}_{1}}=2-i,{{z}_{2}}=2-4i.$ Tính $\left| {{z}_{1}}+{{z}_{1}}.{{z}_{2}} \right|$
A. $\dfrac{\sqrt{5}}{5}$
B. $1.$
C. $5\sqrt{5}$
D. $\sqrt{5}$
A. $\dfrac{\sqrt{5}}{5}$
B. $1.$
C. $5\sqrt{5}$
D. $\sqrt{5}$
Cách giải:
$\left| {{z}_{1}}+{{z}_{1}}.{{z}_{2}} \right|$
$=\left| {{z}_{1}}\left( 1+{{z}_{2}} \right) \right|$
$=\left| {{z}_{1}} \right|.\left| 1+{{z}_{2}} \right|$
$=\left| 2-i \right|.\left| 3-4i \right|$
$=\sqrt{{{2}^{2}}+{{\left( -1 \right)}^{2}}}.\sqrt{{{3}^{2}}+{{\left( -4 \right)}^{2}}}$
$=5\sqrt{5}$
$\left| {{z}_{1}}+{{z}_{1}}.{{z}_{2}} \right|$
$=\left| {{z}_{1}}\left( 1+{{z}_{2}} \right) \right|$
$=\left| {{z}_{1}} \right|.\left| 1+{{z}_{2}} \right|$
$=\left| 2-i \right|.\left| 3-4i \right|$
$=\sqrt{{{2}^{2}}+{{\left( -1 \right)}^{2}}}.\sqrt{{{3}^{2}}+{{\left( -4 \right)}^{2}}}$
$=5\sqrt{5}$
Đáp án C.