Question

The equation $\overline{b}z$+$\overline{z}b=c$ where b is a non-zero complex constant and c is real, represents a

• A. circle
• B. straight line
• C. ellipse
• D. hyperbola

Answer 1

The correct option is B straight line

Equation $\overline{b}z$+$\overline{z}b=c$

$Letz=x+iy,\&b=b_1+i{b}_2$

where $x,y,b_1,b_2$ are real. Then the given equation becomes

$(b_1-i{b}_2)(x+iy)+(b_1+i{b}_2)(x-iy)=c$

$\Rightarrow 2b_{1}x+2b_{2}y=c$

which is equation of a straight line.