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2. 已知 $z=1-2 i$ ，且 $z+a \bar{z}+b=0$ ，其中 $a, b$ 为实数，则（)

Gaokao · Math · previous-year question

  1. A.$a=1, b=-2$correct
  2. B.$a=-1, b=2$
  3. C.$a=1, b=2$
  4. D.$a=-1, b=-2$

Answer

A. $a=1, b=-2$

Explanation

【详解】 $\bar{z}=1+2 \mathrm{i}$ $z+a \bar{z}+b=1-2 \mathrm{i}+a(1+2 \mathrm{i})+b=(1+a+b)+(2 a-2) \mathrm{i}$ 由 $z+a \bar{z}+b=0$, 得 $\left\{\begin{array}{l}1+a+b=0 \\ 2 a-2=0\end{array}\right.$,即 $\left\{\begin{array}{l}a=1 \\ b=-2\end{array}\right.$ 故选: A

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