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Q.
The equation $|z-1|^{2}+|z+1|^{2}=4$ represents on the Argand plane
Complex Numbers and Quadratic Equations
Solution:
We have, $|z-1|^{2}+|z+1|^{2}=4$
$\Rightarrow (x-1)^{2}+y^{2}+(x+1)^{2}+y^{2}=4$
(Putting $z=x+i y$ )
$\Rightarrow 2\left(x^{2}+y^{2}+1\right)=4 $
$\therefore x^{2}+y^{2}=1 $
or $|z|^{2}=1 $
$\Rightarrow |z|=1 $
(since $|z|$ cannot be $- ve$ )
Thus, the Eq. (1) represents all points $z$ on the circle with centre origin and radius unity.