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Q.
If z is a complex number then $|z+1|=\sqrt3|z-1|$ represents
Complex Numbers and Quadratic Equations
Solution:
$\left|z+1\right|^{2}=3\left|z-1\right|^{2}$
$\Rightarrow \left(x+1\right)^{2}+y^{2}=3\left[\left(x-1\right)^{2}+y^{2}\right]$
$\Rightarrow 2\left(x^{2}+y^{2}\right)-8x+2=0$
$\Rightarrow x^{2}+y^{2}-4x+1=0$ which is a circle.