Question

If a is complex number and b is a real number then the equation $a\overline{z}+\overline{a}z+b=0$ represents:

• A. A point
• B. A straight line
• C. A circle
• D. A straight line passing through the origin

Answer 1

The correct option is B A straight line

Let $z=x+iy$ . Let $a=p+iq$

$a\overline{z}=(px+qy)+i(xq-py)$

$\overline{a}z=(px+qy)+i(py-xq)$

Hence,

$a\overline{z}+\overline{a}z+b=2px+2qy+b$

$\Rightarrow px+qy+\frac{b}{2}=0$

This is the equation of a straight line.