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  4. The equation |z-1|2+|z+1|2=2 represents

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Q. The equation $|z-1|^2+|z+1|^2=2$ represents

Complex Numbers and Quadratic Equations

Solution:

$|z-1|^2+|z+1|^2=2$
$z \bar{z}+1-(z+\bar{z})+z \bar{z}+1+(z+\bar{z})=2$
$\Rightarrow z \bar{z}=0$
$\Rightarrow z=0$