Identify the locus of $z$ , if $R e (z + 1) = | z - 1 |$ .

y^{2} = 8 x

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y^{2} = 4 x

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y^{2} = 2 x

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y^{2} = 16 x

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Solution

The correct option is B $y^{2} = 4 x$
$R e (z + 1) = | z - 1 | ⟹ x + 1 = \sqrt{(x - 1)^{2} + y^{2}}$
or $(x + 1)^{2} = (x - 1)^{2} + y^{2}$
or $y^{2} = 4 x$
Ans: B

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