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If $a$ is a complex number and $b$ is a real number, then the equation $\bar{a}+a+b=0$ represents $a$
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Verified Answer
The correct answer is:
straight line
Let $a=x+i y$, then $\bar{a}=x-i y$
Thus,
$\bar{a}+a+b=0$
$\begin{aligned} \Rightarrow & x-i y+x+i y+b & =0 \\ \Rightarrow & 2 x+b & =0 \\ \Rightarrow & x+\frac{b}{2} & =0\end{aligned}$
Which represent a straight line.
Thus,
$\bar{a}+a+b=0$
$\begin{aligned} \Rightarrow & x-i y+x+i y+b & =0 \\ \Rightarrow & 2 x+b & =0 \\ \Rightarrow & x+\frac{b}{2} & =0\end{aligned}$
Which represent a straight line.
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