The locus of the points representing the complex numbers \( z \) for which \( |z|-2=|z-i|-|z+5 i....

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The locus of the points representing the complex
P
numbers \( z \) for which \( |z|-2=|z-i|-|z+5 i|=0 \), is
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(1) a circle with centre at the origin
(2) a straight line passing through the origin
(3) the single point \( (0,-2) \)
(4) None of these


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