Question

If $\overline{a}\ne b$, then the equation $z\overline{z}+az+b\overline{z}+c=0$ represents

• A. A circle
• B. An ellipse
• C. A straight line
• D. Finite number of points in $C$

Answer 1

Answer: (D)

Finite number of points in $C$

Let us take $z=x+iy$
Then $\overline{z}=x-iy$
$z\overline{z}+az+b\overline{z}+c=0=(x+iy)(x-iy)+a(x+iy)+b(x-iy)+c=0$
$=x^2-y^2+ax+aiy+bx-biy+c=0$
This equation is neither circle, nor ellipse nor straight line.