Q137 / 200 · TS EAMCET 2001 · Mathematics

If $a$ is a complex number and $b$ is a real number, then the equation $\bar{a}+a+b=0$ represents $a$

  • Correct answer
    A
    straight line
  • B
    parabola
  • C
    circle
  • D
    hyperbola

Solution

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.

Hence, the correct answer is option: 'A'.

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