Question

If z is a complex number then $|z+1|=\sqrt{3}|z-1|$ represents

• A. Straight line
• B. Ellipse
• C. Hyperbola
• D. circle

Answer 1

Answer: (D)

${\left|z+1\right|}^2=3{\left|z-1\right|}^2$
$\Rightarrow {\left(x+1\right)}^2+y^2=3\left[{\left(x-1\right)}^2+y^2\right]$
$\Rightarrow 2\left(x^2+y^2\right)-8x+2=0$
$\Rightarrow x^2+y^2-4x+1=0$ which is a circle.