Question

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

• A. circle
• B. straight line
• C. one point
• D. ellipse

Answer 1

The correct option is C one point

$az+b{z}^{\prime }+c=0let,z=x+iyand{z}^{\prime }=x-iy,a=e+if,b=g+ih,c=k+il⟹(e+if)(x+iy)+(g+ih)(x-iy)+(k+il)=0⟹(ex-fy+gx+hy+k)+i(fx+ey+hx-gy+l)=0$
By comparing the real and imaginary parts,we get,
$x(e+g)+y(-f+h)+k=0andx(f+h)+y(e-g)+l=0$
These are equations of two straight lines which are not parallel to each other. Hence their intersection will give us one point.