The locus of the point $z$ in the Argand plane for $| z + 1 |^{2} + | z - 1 |^{2} = 4$ is a

Straight line

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Pair Straight Lines

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Circle

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Parabola

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Solution

The correct option is A Circle
Let $z = x + i y$
$| z + 1 |^{2} + | z - 1 |^{2} = | (x + 1) + y i |^{2} + | (x - 1) + y i |^{2} = x^{2} + 2 x + 1 + y^{2} + x^{2} - 2 x + 1 + y^{2} = 4$
$∴$ $x^{2} + y^{2} = 1.$
This is the equation of a circle.

Suggest Corrections

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{log}_{1 / 2} (\frac{| z - 1 | + 4}{3 | z - 1 | - 2}) > 1 (

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