Question

Consider the equation $az+b\overline{z}+c=0$, where $a,b,cϵZ$

If $|a|\ne |b|$ , then $z$ represents

• A. Circle
• B. Ellipse
• C. Straight line
• D. One point

Answer 1

The correct option is D One point

Given:
$az+b\overline{z}+c=0$ , where $a,b,cϵZ$

$az+b\overline{z}+c=0\dots \left(i\right)$

Taking conjugate of (i), we get

$\overline{a}\overline{z}+\overline{b}z+\overline{c}=0\dots \left(ii\right)$

Eliminating $\overline{z}$ from (i) and (ii)

$z=\frac{c\overline{a}-b\overline{c}}{|b{|}^2-|a{|}^2}$

If$|a|\ne |b|,$ then $z$ represents a point on the Argand plane.