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  4. if |z+1|2+|z|2=4, then the locus of z is

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Q. if $|z+1|^2+|z|^2=4$, then the locus of $z$ is

Complex Numbers and Quadratic Equations

Solution:

Put $z=x+i y $
$\Rightarrow(x+1)^2+y^2+x^2+y^2=4 $
$\Rightarrow 2 x^2+2 y^2+2 x-3=0$