Question

Consider the equation $az+b\overline{z}+c=0$, where $a,b,c\in Z$.If $\left|a\right|=\left|b\right|\ne 0$ and $\overline{a}c=b\overline{c}$, then $az+b\overline{z}+c=0$ represents

• A. an ellipse
• B. a circle
• C. a point
• D. a straight line

Answer 1

The correct option is D a straight line

Given, $az+b\overline{z}+c$

$a(x+iy)+b(x-iy)+c=0$
$(a+b)x+iy(a-b)+c=0$
This equation represents straight line.