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Câu hỏi: Có bao nhiêu số phức thoả mãn $z+{{\left| z \right|}^{2}}.i-1-\dfrac{3}{4}i=0?$
A. 1.
B. 3.
C. 2.
D. 0.
A. 1.
B. 3.
C. 2.
D. 0.
Đặt $z=x+yi \left( x,y\in \mathbb{R} \right)$ thì $z+{{\left| z \right|}^{2}}.i-1-\dfrac{3}{4}i=0$
$\Leftrightarrow x+yi+\left( {{x}^{2}}+{{y}^{2}} \right)i-1-\dfrac{3}{4}i=0\Leftrightarrow \left\{ \begin{aligned}
& x-1=0 \\
& y+{{x}^{2}}+{{y}^{2}}-\dfrac{3}{4}=0 \\
\end{aligned} \right.\Leftrightarrow \left\{ \begin{aligned}
& x=1 \\
& y=-\dfrac{1}{2} \\
\end{aligned} \right.\Rightarrow z=1-\dfrac{1}{2}i.$
$\Leftrightarrow x+yi+\left( {{x}^{2}}+{{y}^{2}} \right)i-1-\dfrac{3}{4}i=0\Leftrightarrow \left\{ \begin{aligned}
& x-1=0 \\
& y+{{x}^{2}}+{{y}^{2}}-\dfrac{3}{4}=0 \\
\end{aligned} \right.\Leftrightarrow \left\{ \begin{aligned}
& x=1 \\
& y=-\dfrac{1}{2} \\
\end{aligned} \right.\Rightarrow z=1-\dfrac{1}{2}i.$
Đáp án A.